reserve i,j,k for Nat,
  r,s,r1,r2,s1,s2,sb,tb for Real,
  x for set,
  GX for non empty TopSpace;
reserve GZ for non empty TopSpace;
reserve f for non constant standard special_circular_sequence,
  G for non empty-yielding Matrix of TOP-REAL 2;

theorem Th23:
  G is Y_equal-in-column & 1 <= j & j < width G implies h_strip(G,
  j) = { |[r,s]| : G*(1,j)`2 <= s & s <= G*(1,j+1)`2 }
proof
  assume
A1: G is Y_equal-in-column;
  0 <> len G by MATRIX_0:def 10;
  then
A2: 1 <= len G by NAT_1:14;
  assume 1 <= j & j < width G;
  hence thesis by A1,A2,GOBOARD5:5;
end;
