let E, x be set ; :: thesis: for A being Subset of (E ^omega)
for n being Nat st x in A & x <> <%> E & n > 0 holds
A |^ n <> {(<%> E)}
let A be Subset of (E ^omega); :: thesis: for n being Nat st x in A & x <> <%> E & n > 0 holds
A |^ n <> {(<%> E)}
let n be Nat; :: thesis: ( x in A & x <> <%> E & n > 0 implies A |^ n <> {(<%> E)} )
assume that
A1: ( x in A & x <> <%> E ) and
A2: n > 0 ; :: thesis: A |^ n <> {(<%> E)}
A <> {(<%> E)} by A1, TARSKI:def 1;
hence A |^ n <> {(<%> E)} by A2, FLANG_1:29; :: thesis: verum