%   ORIGINAL: h4/ConseqConv/ASM__MARKER__THM
% 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/ABS__SIMP: !t2 t1. (\x. t1) t2 = t1
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/ConseqConv/ASM__MARKER__DEF: h4/ConseqConv/ASM__MARKER = (\y x. x)
% Goal: !y x. h4/ConseqConv/ASM__MARKER y x <=> x
%   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_ABSu_u_SIMP]: !t2 t1. t1 = t1
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_ConseqConvs_ASMu_u_MARKERu_u_DEF]: !x x'. h4/ConseqConv/ASM__MARKER x x' <=> x'
% Goal: !y x. h4/ConseqConv/ASM__MARKER y x <=> x
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_Q85501,TV_Q85497]: ![V_f, V_g]: (![V_x]: s(TV_Q85497,happ(s(t_fun(TV_Q85501,TV_Q85497),V_f),s(TV_Q85501,V_x))) = s(TV_Q85497,happ(s(t_fun(TV_Q85501,TV_Q85497),V_g),s(TV_Q85501,V_x))) => s(t_fun(TV_Q85501,TV_Q85497),V_f) = s(t_fun(TV_Q85501,TV_Q85497),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ABSu_u_SIMP, axiom, ![TV_u_27b,TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,V_t1) = s(TV_u_27a,V_t1)).
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_ConseqConvs_ASMu_u_MARKERu_u_DEF, axiom, ![V_x, V_xi_]: s(t_bool,h4s_conseqconvs_asmu_u_marker(s(t_bool,V_x),s(t_bool,V_xi_))) = s(t_bool,V_xi_)).
fof(ch4s_ConseqConvs_ASMu_u_MARKERu_u_THM, conjecture, ![V_y, V_x]: s(t_bool,h4s_conseqconvs_asmu_u_marker(s(t_bool,V_y),s(t_bool,V_x))) = s(t_bool,V_x)).
