let i be Nat; :: thesis: for G being empty-yielding Matrix of (TOP-REAL 2) st G is X_equal-in-line & 1 <= i & i < len G holds
v_strip (G,i) = { |[r,s]| where r, s is Real : ( (G * (i,1)) `1 <= r & r <= (G * ((i + 1),1)) `1 ) }
let G be empty-yielding Matrix of (TOP-REAL 2); :: thesis: ( G is X_equal-in-line & 1 <= i & i < len G implies v_strip (G,i) = { |[r,s]| where r, s is Real : ( (G * (i,1)) `1 <= r & r <= (G * ((i + 1),1)) `1 ) } )
assume A1: G is X_equal-in-line ; :: thesis: ( not 1 <= i or not i < len G or v_strip (G,i) = { |[r,s]| where r, s is Real : ( (G * (i,1)) `1 <= r & r <= (G * ((i + 1),1)) `1 ) } )
0 <> width G by MATRIX_0:def 10;
then A2: 1 <= width G by NAT_1:14;
assume ( 1 <= i & i < len G ) ; :: thesis: v_strip (G,i) = { |[r,s]| where r, s is Real : ( (G * (i,1)) `1 <= r & r <= (G * ((i + 1),1)) `1 ) }
hence v_strip (G,i) = { |[r,s]| where r, s is Real : ( (G * (i,1)) `1 <= r & r <= (G * ((i + 1),1)) `1 ) } by A1, A2, GOBOARD5:8; :: thesis: verum