let f be set ; :: thesis: for p being FinSequence holds
( the Arity of (1GateCircStr p,f) = p,f .--> p & the ResultSort of (1GateCircStr p,f) = p,f .--> [p,f] )
let p be FinSequence; :: thesis: ( the Arity of (1GateCircStr p,f) = p,f .--> p & the ResultSort of (1GateCircStr p,f) = p,f .--> [p,f] )
set S = 1GateCircStr p,f;
the Arity of (1GateCircStr p,f) . [p,f] = p by Def6;
then A1: for x being set st x in {[p,f]} holds
the Arity of (1GateCircStr p,f) . x = p by TARSKI:def 1;
A2: the carrier' of (1GateCircStr p,f) = {[p,f]} by Def6;
then dom the Arity of (1GateCircStr p,f) = {[p,f]} by FUNCT_2:def 1;
hence the Arity of (1GateCircStr p,f) = p,f .--> p by A1, FUNCOP_1:17; :: thesis: the ResultSort of (1GateCircStr p,f) = p,f .--> [p,f]
the ResultSort of (1GateCircStr p,f) . [p,f] = [p,f] by Def6;
then A3: for x being set st x in {[p,f]} holds
the ResultSort of (1GateCircStr p,f) . x = [p,f] by TARSKI:def 1;
dom the ResultSort of (1GateCircStr p,f) = {[p,f]} by A2, FUNCT_2:def 1;
hence the ResultSort of (1GateCircStr p,f) = p,f .--> [p,f] by A3, FUNCOP_1:17; :: thesis: verum