let S be non empty non void bool-correct 4,1 integer BoolSignature ; :: thesis: for I being integer SortSymbol of S
for o being OperSymbol of S st o = In (( the connectives of S . 10), the carrier' of S) holds
( the_arity_of o = <*I,I*> & the_result_sort_of o = the bool-sort of S )
let I be integer SortSymbol of S; :: thesis: for o being OperSymbol of S st o = In (( the connectives of S . 10), the carrier' of S) holds
( the_arity_of o = <*I,I*> & the_result_sort_of o = the bool-sort of S )
let o be OperSymbol of S; :: thesis: ( o = In (( the connectives of S . 10), the carrier' of S) implies ( the_arity_of o = <*I,I*> & the_result_sort_of o = the bool-sort of S ) )
assume A1: o = In (( the connectives of S . 10), the carrier' of S) ; :: thesis: ( the_arity_of o = <*I,I*> & the_result_sort_of o = the bool-sort of S )
4 + 6 <= len the connectives of S by AOFA_A00:def 39;
then 10 in dom the connectives of S by FINSEQ_3:25;
then o = the connectives of S . 10 by A1, FUNCT_1:102, SUBSET_1:def 8;
then o is_of_type <*I,I*>, the bool-sort of S by AOFA_A00:53;
hence ( the_arity_of o = <*I,I*> & the_result_sort_of o = the bool-sort of S ) ; :: thesis: verum