%   ORIGINAL: 'h4/thm/arithmetic/NUMERAL_MULT_EQ_DIV_e1'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !z y x. 'h4/const/arithmetic/*' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' x)) y = 'h4/const/arithmetic/NUMERAL' z <=> y = 'h4/const/arithmetic/DIV' ('h4/const/arithmetic/NUMERAL' z) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' x)) /\ 'h4/const/arithmetic/MOD' ('h4/const/arithmetic/NUMERAL' z) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' x)) = 'h4/const/num/0'
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !z y x. 'h4/const/arithmetic/*' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' x)) y = 'h4/const/arithmetic/NUMERAL' z <=> y = 'h4/const/arithmetic/DIV' ('h4/const/arithmetic/NUMERAL' z) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' x)) /\ 'h4/const/arithmetic/MOD' ('h4/const/arithmetic/NUMERAL' z) ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT2' x)) = 'h4/const/num/0'
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f82941,V_3f82937]: ![F, G]: (![X]: s(V_3f82937,happ(s(fun(V_3f82941,V_3f82937),F),s(V_3f82941,X))) = s(V_3f82937,happ(s(fun(V_3f82941,V_3f82937),G),s(V_3f82941,X))) => s(fun(V_3f82941,V_3f82937),F) = s(fun(V_3f82941,V_3f82937),G))).
fof('h4/thm/arithmetic/NUMERAL_MULT_EQ_DIV_e1', conjecture, ![Z, Y, X]: (s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num',X))))),s('h4/type/num/num',Y))) = s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num',Z))) <=> (s('h4/type/num/num',Y) = s('h4/type/num/num','h4/const/arithmetic/DIV'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num',Z))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num',X))))))) & s('h4/type/num/num','h4/const/arithmetic/MOD'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num',Z))),s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT2'(s('h4/type/num/num',X))))))) = s('h4/type/num/num','h4/const/num/0')))).
