for F being ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) holds (revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . (1. F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) : ( ( ) ( ) set ) = 1. F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ;

for F being ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field)
for a, b being ( ( ) ( ) Element of NonZero F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) holds (revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . ((omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (a : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ,((revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . b : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) set ) : ( ( ) ( ) set ) = (omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (b : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ,((revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . a : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ;

for F being ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field)
for a, b being ( ( ) ( ) Element of NonZero F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) holds (revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . ((omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (a : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ,b : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) : ( ( ) ( ) set ) = (omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (((revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . a : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ,((revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . b : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) ;

for F being ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field)
for a, b, c, d being ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) holds
( a : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) - b : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) = c : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) - d : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) iff a : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) + d : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) = b : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) + c : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) ;

for F being ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field)
for a, c being ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) )
for b, d being ( ( ) ( ) Element of NonZero F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) holds
( (omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (a : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) ,((revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . b : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) = (omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (c : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) ,((revf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) ( V1() V4( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) V5( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) Function-like V18( NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) , NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) Element of bool [:(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ,(NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) . d : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) set ) iff (omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (a : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) ,d : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) = (omf F : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) : ( ( ) ( V1() V4([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) ) V5( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) Function-like V18([: the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) :] : ( ( ) ( ) set ) , the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) M10( the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) , 0. b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V51(b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) ) ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) )) . (b : ( ( ) ( ) Element of NonZero b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() ) Element of bool the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) : ( ( ) ( ) set ) ) ) ,c : ( ( ) ( ) Element of ( ( ) ( V11() non trivial ) set ) ) ) : ( ( ) ( ) Element of the carrier of b₁ : ( ( V44() non degenerated right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() ) ( V44() non degenerated non trivial right_complementable almost_left_invertible V95() V96() V97() associative commutative well-unital V114() Field-like ) Field) : ( ( ) ( V11() non trivial ) set ) ) ) ;