%   ORIGINAL: 'h4/thm/hreal/HREAL_LDISTRIB_'
% 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: !X Y Z. 'h4/const/hreal/hreal_mul' X ('h4/const/hreal/hreal_add' Y Z) = 'h4/const/hreal/hreal_add' ('h4/const/hreal/hreal_mul' X Y) ('h4/const/hreal/hreal_mul' X Z)
%   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: !X Y Z. 'h4/const/hreal/hreal_mul' X ('h4/const/hreal/hreal_add' Y Z) = 'h4/const/hreal/hreal_add' ('h4/const/hreal/hreal_mul' X Y) ('h4/const/hreal/hreal_mul' X Z)
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_3f37079,V_3f37075]: ![F, G]: (![X]: s(V_3f37075,happ(s(fun(V_3f37079,V_3f37075),F),s(V_3f37079,X))) = s(V_3f37075,happ(s(fun(V_3f37079,V_3f37075),G),s(V_3f37079,X))) => s(fun(V_3f37079,V_3f37075),F) = s(fun(V_3f37079,V_3f37075),G))).
fof('h4/thm/hreal/HREAL_LDISTRIB_', conjecture, ![X, Y, Z]: s('h4/type/hreal/hreal','h4/const/hreal/hreal_mul'(s('h4/type/hreal/hreal',X),s('h4/type/hreal/hreal','h4/const/hreal/hreal_add'(s('h4/type/hreal/hreal',Y),s('h4/type/hreal/hreal',Z))))) = s('h4/type/hreal/hreal','h4/const/hreal/hreal_add'(s('h4/type/hreal/hreal','h4/const/hreal/hreal_mul'(s('h4/type/hreal/hreal',X),s('h4/type/hreal/hreal',Y))),s('h4/type/hreal/hreal','h4/const/hreal/hreal_mul'(s('h4/type/hreal/hreal',X),s('h4/type/hreal/hreal',Z)))))).
