%   ORIGINAL: h4/hrat/TRAT__MUL__SYM
% 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/hrat/TRAT__EQ__AP: !q p. p = q ==> h4/hrat/trat__eq p q
% Assm: h4/hrat/TRAT__MUL__SYM__EQ: !i h. h4/hrat/trat__mul h i = h4/hrat/trat__mul i h
% Goal: !i h. h4/hrat/trat__eq (h4/hrat/trat__mul h i) (h4/hrat/trat__mul i h)
%   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_hrats_TRATu_u_EQu_u_AP]: !q p. p = q ==> h4/hrat/trat__eq p q
% Assm [h4s_hrats_TRATu_u_MULu_u_SYMu_u_EQ]: !i h. h4/hrat/trat__mul h i = h4/hrat/trat__mul i h
% Goal: !i h. h4/hrat/trat__eq (h4/hrat/trat__mul h i) (h4/hrat/trat__mul i h)
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_Q86853,TV_Q86849]: ![V_f, V_g]: (![V_x]: s(TV_Q86849,happ(s(t_fun(TV_Q86853,TV_Q86849),V_f),s(TV_Q86853,V_x))) = s(TV_Q86849,happ(s(t_fun(TV_Q86853,TV_Q86849),V_g),s(TV_Q86853,V_x))) => s(t_fun(TV_Q86853,TV_Q86849),V_f) = s(t_fun(TV_Q86853,TV_Q86849),V_g))).
fof(ah4s_hrats_TRATu_u_EQu_u_AP, axiom, ![V_q, V_p]: (s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_p) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_q) => p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_p),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_q)))))).
fof(ah4s_hrats_TRATu_u_MULu_u_SYMu_u_EQ, axiom, ![V_i, V_h]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_h),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_i))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_i),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_h)))).
fof(ch4s_hrats_TRATu_u_MULu_u_SYM, conjecture, ![V_i, V_h]: p(s(t_bool,h4s_hrats_tratu_u_eq(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_h),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_i))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_i),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_h))))))).
