:: GOBOARD4 semantic presentation

begin

theorem :: GOBOARD4:1
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board)
for f1, f2 being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is_sequence_on G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is_sequence_on G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Line (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((width b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Line (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((width b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Col (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((len b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Col (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((len b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) holds
rng f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) meets rng f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ;

theorem :: GOBOARD4:2
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board)
for f1, f2 being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is_sequence_on G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is_sequence_on G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Line (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((width b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Line (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((width b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Col (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((len b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Col (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((len b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) holds
L~ f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) meets L~ f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD4:3
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board)
for f1, f2 being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is_sequence_on G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is_sequence_on G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Line (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((width b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Line (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((width b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Col (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((len b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) in rng (Col (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) M11( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ,K180((len b1 : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( Relation-like non empty-yielding NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined K179( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) -valued Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) , the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional FinSequence-membered ) M10( the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) )) )) : ( ( ) ( ) set ) holds
L~ f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) meets L~ f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;

definition
let f be ( ( Relation-like ) ( Relation-like ) Relation) ;
let r, s be ( ( ) ( ext-real V14() V15() ) Real) ;
pred f lies_between r,s means :: GOBOARD4:def 1
 rng f : ( ( ) ( ) TopStruct ) : ( ( ) ( ) set ) c= [.r : ( ( ) ( ) Element of bool (bool f : ( ( ) ( ) TopStruct ) ) : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) ,s : ( ( ) ( ) set ) .] : ( ( ) ( ) set ) ;
end;

definition
let f be ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ;
let r, s be ( ( ) ( ext-real V14() V15() ) Real) ;
redefine pred f lies_between r,s means :: GOBOARD4:def 2
 for n being ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) st n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) in dom f : ( ( ) ( ) TopStruct ) : ( ( ) ( V146() V147() V148() V149() V150() V151() ) Element of bool NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) : ( ( ) ( V33() ) set ) ) holds
( r : ( ( ) ( ) Element of bool (bool f : ( ( ) ( ) TopStruct ) ) : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) <= f : ( ( ) ( ) TopStruct ) . n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & f : ( ( ) ( ) TopStruct ) . n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) <= s : ( ( ) ( ) set ) );
end;

theorem :: GOBOARD4:4
for f1, f2 being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is special & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is special & ( for n being ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) st n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) in dom f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V146() V147() V148() V149() V150() V151() ) Element of bool NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) : ( ( ) ( V33() ) set ) ) & n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) + 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) in dom f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V146() V147() V148() V149() V150() V151() ) Element of bool NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) : ( ( ) ( V33() ) set ) ) holds
f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) <> f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) + 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) ) & ( for n being ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) st n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) in dom f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V146() V147() V148() V149() V150() V151() ) Element of bool NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) : ( ( ) ( V33() ) set ) ) & n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) + 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) in dom f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V146() V147() V148() V149() V150() V151() ) Element of bool NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) : ( ( ) ( V33() ) set ) ) holds
f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) <> f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (n : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) + 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) ) ) & X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & X_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & Y_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) holds
L~ f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) meets L~ f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD4:5
for f1, f2 being ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is one-to-one & f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is special & 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is one-to-one & f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is special & 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) <= len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) & X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & X_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(X_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & Y_axis f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) lies_between (Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . 1 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ,(Y_axis f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like V136() V137() V138() ) FinSequence of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) . (len f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) holds
L~ f1 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) meets L~ f2 : ( ( ) ( Relation-like NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) -defined the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD4:6
for P1, P2 being ( ( ) ( ) Subset of )
for p1, p2, q1, q2 being ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) st P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p1 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) ,q1 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) & P2 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p2 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) ,q2 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) & ( for p being ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) in P1 : ( ( ) ( ) Subset of ) \/ P2 : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) holds
( p1 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) <= p : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) <= q1 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ) ) & ( for p being ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) in P1 : ( ( ) ( ) Subset of ) \/ P2 : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the U1 of (TOP-REAL 2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) : ( ( V170() ) ( non empty TopSpace-like V112() V158() V159() V160() V161() V162() V163() V164() V170() ) L15()) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) holds
( p2 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) <= p : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) <= q2 : ( ( ) ( V40(2 : ( ( ) ( ext-real positive non empty V7() V8() V9() V13() V14() V15() V33() V38() V83() V84() V146() V147() V148() V149() V150() V151() ) Element of NAT : ( ( ) ( non empty V7() V8() V9() V33() V38() V39() V146() V147() V148() V149() V150() V151() V152() ) Element of bool REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) : ( ( ) ( V33() ) set ) ) ) ) FinSequence-like V138() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V14() V15() ) Element of REAL : ( ( ) ( non empty V33() V146() V147() V148() V152() ) set ) ) ) ) holds
P1 : ( ( ) ( ) Subset of ) meets P2 : ( ( ) ( ) Subset of ) ;