let S be non empty non void bool-correct 4,1 integer BoolSignature ; for I being integer SortSymbol of S
for o being OperSymbol of S st o = In (( the connectives of S . 8), the carrier' of S) holds
( the_arity_of o = <*I,I*> & the_result_sort_of o = I )
let I be integer SortSymbol of S; for o being OperSymbol of S st o = In (( the connectives of S . 8), the carrier' of S) holds
( the_arity_of o = <*I,I*> & the_result_sort_of o = I )
let o be OperSymbol of S; ( o = In (( the connectives of S . 8), the carrier' of S) implies ( the_arity_of o = <*I,I*> & the_result_sort_of o = I ) )
assume A1:
o = In (( the connectives of S . 8), the carrier' of S)
; ( the_arity_of o = <*I,I*> & the_result_sort_of o = I )
4 + 6 <= len the connectives of S
by AOFA_A00:def 39;
then
8 <= len the connectives of S
by XXREAL_0:2;
then
8 in dom the connectives of S
by FINSEQ_3:25;
then
o = the connectives of S . 8
by A1, FUNCT_1:102, SUBSET_1:def 8;
then
o is_of_type <*I,I*>,I
by AOFA_A00:53;
hence
( the_arity_of o = <*I,I*> & the_result_sort_of o = I )
; verum