%   ORIGINAL: h4/quotient/NOT__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/FALSITY: !t. F ==> t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Goal: !Q P. (Q ==> P) ==> ~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_FALSITY]: !t. F ==> t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Goal: !Q P. (Q ==> P) ==> ~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_Q226183,TV_Q226179]: ![V_f, V_g]: (![V_x]: s(TV_Q226179,happ(s(t_fun(TV_Q226183,TV_Q226179),V_f),s(TV_Q226183,V_x))) = s(TV_Q226179,happ(s(t_fun(TV_Q226183,TV_Q226179),V_g),s(TV_Q226183,V_x))) => s(t_fun(TV_Q226183,TV_Q226179),V_f) = s(t_fun(TV_Q226183,TV_Q226179),V_g))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ch4s_quotients_NOTu_u_IMPLIES, conjecture, ![V_Q, V_P]: ((p(s(t_bool,V_Q)) => p(s(t_bool,V_P))) => (~ (p(s(t_bool,V_P))) => ~ (p(s(t_bool,V_Q)))))).
