%   ORIGINAL: h4/realax/HREAL__RDISTRIB
% 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
% Assm: h4/hreal/HREAL__MUL__SYM: !Y X. h4/hreal/hreal__mul X Y = h4/hreal/hreal__mul Y X
% Assm: h4/hreal/HREAL__LDISTRIB: !Z Y X. h4/hreal/hreal__mul X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__mul X Y) (h4/hreal/hreal__mul X Z)
% Goal: !z y x. h4/hreal/hreal__mul (h4/hreal/hreal__add x y) z = h4/hreal/hreal__add (h4/hreal/hreal__mul x z) (h4/hreal/hreal__mul y z)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_hreals_HREALu_u_MULu_u_SYM]: !Y X. h4/hreal/hreal__mul X Y = h4/hreal/hreal__mul Y X
% Assm [h4s_hreals_HREALu_u_LDISTRIB]: !Z Y X. h4/hreal/hreal__mul X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__mul X Y) (h4/hreal/hreal__mul X Z)
% Goal: !z y x. h4/hreal/hreal__mul (h4/hreal/hreal__add x y) z = h4/hreal/hreal__add (h4/hreal/hreal__mul x z) (h4/hreal/hreal__mul y z)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q328114,TV_Q328110]: ![V_f, V_g]: (![V_x]: s(TV_Q328110,happ(s(t_fun(TV_Q328114,TV_Q328110),V_f),s(TV_Q328114,V_x))) = s(TV_Q328110,happ(s(t_fun(TV_Q328114,TV_Q328110),V_g),s(TV_Q328114,V_x))) => s(t_fun(TV_Q328114,TV_Q328110),V_f) = s(t_fun(TV_Q328114,TV_Q328110),V_g))).
fof(ah4s_hreals_HREALu_u_MULu_u_SYM, axiom, ![V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_X)))).
fof(ah4s_hreals_HREALu_u_LDISTRIB, axiom, ![V_Z, V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_Z))))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Z)))))).
fof(ch4s_realaxs_HREALu_u_RDISTRIB, conjecture, ![V_z, V_y, V_x]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))),s(t_h4s_hreals_hreal,V_z))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_z))),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_y),s(t_h4s_hreals_hreal,V_z)))))).
