%   ORIGINAL: h4/set__relation/reln__rel__conv__thms_c4
% 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/set__relation/reln__to__rel__11: !r2 r1. h4/set__relation/reln__to__rel r1 = h4/set__relation/reln__to__rel r2 <=> r1 = r2
% Goal: !r2 r1. h4/set__relation/reln__to__rel r1 = h4/set__relation/reln__to__rel r2 <=> r1 = r2
%   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_setu_u_relations_relnu_u_tou_u_relu_u_11]: !r2 r1. h4/set__relation/reln__to__rel r1 = h4/set__relation/reln__to__rel r2 <=> r1 = r2
% Goal: !r2 r1. h4/set__relation/reln__to__rel r1 = h4/set__relation/reln__to__rel r2 <=> r1 = r2
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_Q139876,TV_Q139872]: ![V_f, V_g]: (![V_x]: s(TV_Q139872,happ(s(t_fun(TV_Q139876,TV_Q139872),V_f),s(TV_Q139876,V_x))) = s(TV_Q139872,happ(s(t_fun(TV_Q139876,TV_Q139872),V_g),s(TV_Q139876,V_x))) => s(t_fun(TV_Q139876,TV_Q139872),V_f) = s(t_fun(TV_Q139876,TV_Q139872),V_g))).
fof(ah4s_setu_u_relations_relnu_u_tou_u_relu_u_11, axiom, ![TV_u_27a,TV_u_27b]: ![V_r2, V_r1]: (s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r1))) = s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r2))) <=> s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r1) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r2))).
fof(ch4s_setu_u_relations_relnu_u_relu_u_convu_u_thmsu_c4, conjecture, ![TV_u_27a,TV_u_27b]: ![V_r2, V_r1]: (s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r1))) = s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),h4s_setu_u_relations_relnu_u_tou_u_rel(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r2))) <=> s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r1) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_r2))).
