let n be Nat; :: thesis: for ap, bp, cp, dp being FinSequence holds [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] in InnerVertices (n -BitFTA0Layer2Str (ap,bp,cp,dp))
let ap, bp, cp, dp be FinSequence; :: thesis: [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] in InnerVertices (n -BitFTA0Layer2Str (ap,bp,cp,dp))
set c0 = [<*>,((0 -tuples_on BOOLEAN) --> FALSE)];
defpred S₁[ Nat] means [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] in InnerVertices ($1 -BitFTA0Layer2Str (ap,bp,cp,dp));
0 -BitFTA0Layer2Str (ap,bp,cp,dp) = 1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE)) by LmT00L2;
then InnerVertices (0 -BitFTA0Layer2Str (ap,bp,cp,dp)) = {[<*>,((0 -tuples_on BOOLEAN) --> FALSE)]} by CIRCCOMB:42;
then A1: S₁[ 0 ] by TARSKI:def 1;
A2: for i being Nat st S₁[i] holds
S₁[i + 1]

proof

let i be Nat; :: thesis: ( S₁[i] implies S₁[i + 1] )
assume S₁[i] ; :: thesis: S₁[i + 1]
then [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] in (InnerVertices (i -BitFTA0Layer2Str (ap,bp,cp,dp))) \/ (InnerVertices (BitGFA0Str ((GFA0AdderOutput ((ap . (i + 1)),(bp . (i + 1)),(cp . (i + 1)))),(i -BitFTA0CarryOutput (ap,bp,cp,dp)),(dp . (i + 1))))) by XBOOLE_0:def 3;
hence S₁[i + 1] by LmT0L2inner; :: thesis: verum

end;

for i being Nat holds S₁[i] from NAT_1:sch 2(A1, A2);
hence [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] in InnerVertices (n -BitFTA0Layer2Str (ap,bp,cp,dp)) ; :: thesis: verum