%   ORIGINAL: 'h4/thm/hrat/TRAT_MUL_WELLDEFINED_'
% 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: !p q r. 'h4/const/hrat/trat_eq' p q ==> 'h4/const/hrat/trat_eq' ('h4/const/hrat/trat_mul' p r) ('h4/const/hrat/trat_mul' q r)
%   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: !p q r. 'h4/const/hrat/trat_eq' p q ==> 'h4/const/hrat/trat_eq' ('h4/const/hrat/trat_mul' p r) ('h4/const/hrat/trat_mul' q r)
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_3f13394,V_3f13390]: ![F, G]: (![X]: s(V_3f13390,happ(s(fun(V_3f13394,V_3f13390),F),s(V_3f13394,X))) = s(V_3f13390,happ(s(fun(V_3f13394,V_3f13390),G),s(V_3f13394,X))) => s(fun(V_3f13394,V_3f13390),F) = s(fun(V_3f13394,V_3f13390),G))).
fof('h4/thm/hrat/TRAT_MUL_WELLDEFINED_', conjecture, ![P, Q, R]: (p(s(bool,'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),P),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),Q)))) => p(s(bool,'h4/const/hrat/trat_eq'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/hrat/trat_mul'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),P),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),R))),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/hrat/trat_mul'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),Q),s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),R)))))))).
