let f be FinSequence of (TOP-REAL 2); :: thesis: for m being Element of NAT
for G being Go-board st m in dom f & f /. m in rng (Col G,(width G)) holds
(f | m) /. (len (f | m)) in rng (Col G,(width G))
let m be Element of NAT ; :: thesis: for G being Go-board st m in dom f & f /. m in rng (Col G,(width G)) holds
(f | m) /. (len (f | m)) in rng (Col G,(width G))
let G be Go-board; :: thesis: ( m in dom f & f /. m in rng (Col G,(width G)) implies (f | m) /. (len (f | m)) in rng (Col G,(width G)) )
assume that
A1: m in dom f and
A2: f /. m in rng (Col G,(width G)) ; :: thesis: (f | m) /. (len (f | m)) in rng (Col G,(width G))
m <= len f by A1, FINSEQ_3:27;
then A3: len (f | m) = m by FINSEQ_1:80;
1 <= m by A1, FINSEQ_3:27;
then m in Seg m by FINSEQ_1:3;
hence (f | m) /. (len (f | m)) in rng (Col G,(width G)) by A1, A2, A3, FINSEQ_4:86; :: thesis: verum