let G be Go-board; :: thesis: for f being FinSequence of (TOP-REAL 2) st f is_sequence_on G & f is special holds
for i, j being Element of NAT st i <= len G & j <= width G holds
Int (cell G,i,j) c= (L~ f) `
let f be FinSequence of (TOP-REAL 2); :: thesis: ( f is_sequence_on G & f is special implies for i, j being Element of NAT st i <= len G & j <= width G holds
Int (cell G,i,j) c= (L~ f) ` )
assume A1: ( f is_sequence_on G & f is special ) ; :: thesis: for i, j being Element of NAT st i <= len G & j <= width G holds
Int (cell G,i,j) c= (L~ f) `
let i, j be Element of NAT ; :: thesis: ( i <= len G & j <= width G implies Int (cell G,i,j) c= (L~ f) ` )
assume ( i <= len G & j <= width G ) ; :: thesis: Int (cell G,i,j) c= (L~ f) `
then Int (cell G,i,j) misses L~ f by A1, JORDAN9:16;
hence Int (cell G,i,j) c= (L~ f) ` by SUBSET_1:43; :: thesis: verum