%   ORIGINAL: h4/rat/RAT__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
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/rat/RAT__MUL__COMM: !b a. h4/rat/rat__mul a b = h4/rat/rat__mul b a
% Assm: h4/rat/RAT__RDISTRIB: !c b a. h4/rat/rat__mul (h4/rat/rat__add a b) c = h4/rat/rat__add (h4/rat/rat__mul a c) (h4/rat/rat__mul b c)
% Goal: !c b a. h4/rat/rat__mul c (h4/rat/rat__add a b) = h4/rat/rat__add (h4/rat/rat__mul c a) (h4/rat/rat__mul c b)
%   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_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_rats_RATu_u_MULu_u_COMM]: !b a. h4/rat/rat__mul a b = h4/rat/rat__mul b a
% Assm [h4s_rats_RATu_u_RDISTRIB]: !c b a. h4/rat/rat__mul (h4/rat/rat__add a b) c = h4/rat/rat__add (h4/rat/rat__mul a c) (h4/rat/rat__mul b c)
% Goal: !c b a. h4/rat/rat__mul c (h4/rat/rat__add a b) = h4/rat/rat__add (h4/rat/rat__mul c a) (h4/rat/rat__mul c b)
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_Q92820,TV_Q92816]: ![V_f, V_g]: (![V_x]: s(TV_Q92816,happ(s(t_fun(TV_Q92820,TV_Q92816),V_f),s(TV_Q92820,V_x))) = s(TV_Q92816,happ(s(t_fun(TV_Q92820,TV_Q92816),V_g),s(TV_Q92820,V_x))) => s(t_fun(TV_Q92820,TV_Q92816),V_f) = s(t_fun(TV_Q92820,TV_Q92816),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_rats_RATu_u_MULu_u_COMM, axiom, ![V_b, V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,V_b))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_b),s(t_h4s_rats_rat,V_a)))).
fof(ah4s_rats_RATu_u_RDISTRIB, axiom, ![V_c, V_b, V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,V_b))),s(t_h4s_rats_rat,V_c))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,V_c))),s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_b),s(t_h4s_rats_rat,V_c)))))).
fof(ch4s_rats_RATu_u_LDISTRIB, conjecture, ![V_c, V_b, V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_c),s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,V_b))))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_c),s(t_h4s_rats_rat,V_a))),s(t_h4s_rats_rat,h4s_rats_ratu_u_mul(s(t_h4s_rats_rat,V_c),s(t_h4s_rats_rat,V_b)))))).
