%   ORIGINAL: 'h4/thm/relation/IN_RDOM_RUNION_'
% 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
% Goal: !x R2 R1. 'h4/const/bool/IN' x ('h4/const/relation/RDOM' ('h4/const/relation/RUNION' R1 R2)) <=> 'h4/const/bool/IN' x ('h4/const/relation/RDOM' R1) \/ 'h4/const/bool/IN' x ('h4/const/relation/RDOM' R2)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !x R2 R1. 'h4/const/bool/IN' x ('h4/const/relation/RDOM' ('h4/const/relation/RUNION' R1 R2)) <=> 'h4/const/bool/IN' x ('h4/const/relation/RDOM' R1) \/ 'h4/const/bool/IN' x ('h4/const/relation/RDOM' R2)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f30353,V_3f30349]: ![F, G]: (![X]: s(V_3f30349,happ(s(fun(V_3f30353,V_3f30349),F),s(V_3f30353,X))) = s(V_3f30349,happ(s(fun(V_3f30353,V_3f30349),G),s(V_3f30353,X))) => s(fun(V_3f30353,V_3f30349),F) = s(fun(V_3f30353,V_3f30349),G))).
fof('h4/thm/relation/IN_RDOM_RUNION_', conjecture, ![A,B]: ![X, R2, R1]: (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/relation/RDOM'(s(fun(A,fun(B,bool)),'h4/const/relation/RUNION'(s(fun(A,fun(B,bool)),R1),s(fun(A,fun(B,bool)),R2)))))))) <=> (p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/relation/RDOM'(s(fun(A,fun(B,bool)),R1)))))) | p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/relation/RDOM'(s(fun(A,fun(B,bool)),R2))))))))).
