environ
vocabularies HIDDEN, STRUCT_0, XBOOLE_0, MSUALG_1, RELAT_1, PBOOLE, MEMBER_1, TARSKI, REALSET1, FUNCT_1, PZFMISC1, MSUALG_3, FUNCT_6, MSAFREE, LANG1, MCART_1, TREES_4, SUBSET_1, FUNCOP_1, PRELAMB, MSUALG_2, UNIALG_2, MARGREL1, CARD_3, NAT_1, PARTFUN1;
notations HIDDEN, TARSKI, XBOOLE_0, SUBSET_1, RELAT_1, RELSET_1, FUNCT_1, XTUPLE_0, MCART_1, PARTFUN1, FUNCOP_1, FUNCT_6, PZFMISC1, FINSEQ_2, STRUCT_0, LANG1, FUNCT_2, CARD_3, ORDINAL1, TREES_4, DTCONSTR, PBOOLE, MSUALG_1, MSUALG_2, MSUALG_3, MSAFREE;
definitions MSUALG_2, MSUALG_3, PBOOLE, FUNCOP_1, TARSKI, XBOOLE_0;
theorems FUNCOP_1, FUNCT_1, FUNCT_2, FUNCT_6, MSAFREE, MSAFREE2, MSUALG_1, MSUALG_2, MSUALG_3, MSUHOM_1, PBOOLE, RELAT_1, CARD_3, RELSET_1, PZFMISC1, ORDINAL1, PARTFUN1, FINSEQ_2;
schemes MSAFREE1, PBOOLE;
registrations FUNCT_1, RELSET_1, FUNCOP_1, PBOOLE, STRUCT_0, MSUALG_1, MSUALG_3, MSAFREE, MSSUBFAM, FINSEQ_1, XTUPLE_0;
constructors HIDDEN, PZFMISC1, MSUALG_3, MSAFREE, RELSET_1, XTUPLE_0;
requirements HIDDEN, SUBSET, BOOLE;
equalities XBOOLE_0;
expansions MSUALG_3, PBOOLE;
Lm1:
for I being set
for A, B, C being ManySortedSet of I
for F being ManySortedFunction of A,B
for G being ManySortedFunction of B,C holds G ** F is ManySortedSet of I