%   ORIGINAL: h4/quotient/EQ__IMPLIES
% 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/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Goal: !Q P. (P <=> Q) ==> P ==> Q
%   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_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Goal: !Q P. (P <=> Q) ==> P ==> Q
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_Q226058,TV_Q226054]: ![V_f, V_g]: (![V_x]: s(TV_Q226054,happ(s(t_fun(TV_Q226058,TV_Q226054),V_f),s(TV_Q226058,V_x))) = s(TV_Q226054,happ(s(t_fun(TV_Q226058,TV_Q226054),V_g),s(TV_Q226058,V_x))) => s(t_fun(TV_Q226058,TV_Q226054),V_f) = s(t_fun(TV_Q226058,TV_Q226054),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ch4s_quotients_EQu_u_IMPLIES, conjecture, ![V_Q, V_P]: (s(t_bool,V_P) = s(t_bool,V_Q) => (p(s(t_bool,V_P)) => p(s(t_bool,V_Q))))).
