%   ORIGINAL: h4/pred__set/DISJOINT__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/pred__set/INTER__COMM: !t s. h4/pred__set/INTER s t = h4/pred__set/INTER t s
% Assm: h4/pred__set/DISJOINT__DEF: !t s. h4/pred__set/DISJOINT s t <=> h4/pred__set/INTER s t = h4/pred__set/EMPTY
% Goal: !t s. h4/pred__set/DISJOINT s t <=> h4/pred__set/DISJOINT t s
%   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_predu_u_sets_INTERu_u_COMM]: !t s. h4/pred__set/INTER s t = h4/pred__set/INTER t s
% Assm [h4s_predu_u_sets_DISJOINTu_u_DEF]: !t s. h4/pred__set/DISJOINT s t <=> h4/pred__set/INTER s t = h4/pred__set/EMPTY
% Goal: !t s. h4/pred__set/DISJOINT s t <=> h4/pred__set/DISJOINT t s
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q148023,TV_Q148019]: ![V_f, V_g]: (![V_x]: s(TV_Q148019,happ(s(t_fun(TV_Q148023,TV_Q148019),V_f),s(TV_Q148023,V_x))) = s(TV_Q148019,happ(s(t_fun(TV_Q148023,TV_Q148019),V_g),s(TV_Q148023,V_x))) => s(t_fun(TV_Q148023,TV_Q148019),V_f) = s(t_fun(TV_Q148023,TV_Q148019),V_g))).
fof(ah4s_predu_u_sets_INTERu_u_COMM, axiom, ![TV_u_27a]: ![V_t, V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_s)))).
fof(ah4s_predu_u_sets_DISJOINTu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))).
fof(ch4s_predu_u_sets_DISJOINTu_u_SYM, conjecture, ![TV_u_27a]: ![V_t, V_s]: s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))) = s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_s)))).
