%   ORIGINAL: 'h4/thm/rich_list/EL_REPLICATE_'
% 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: !n1 n2 x. 'h4/const/prim_rec/<' n1 n2 ==> 'h4/const/list/EL' n1 ('h4/const/rich_list/REPLICATE' n2 x) = x
%   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: !n1 n2 x. 'h4/const/prim_rec/<' n1 n2 ==> 'h4/const/list/EL' n1 ('h4/const/rich_list/REPLICATE' n2 x) = x
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_3f57736,V_3f57732]: ![F, G]: (![X]: s(V_3f57732,happ(s(fun(V_3f57736,V_3f57732),F),s(V_3f57736,X))) = s(V_3f57732,happ(s(fun(V_3f57736,V_3f57732),G),s(V_3f57736,X))) => s(fun(V_3f57736,V_3f57732),F) = s(fun(V_3f57736,V_3f57732),G))).
fof('h4/thm/rich_list/EL_REPLICATE_', conjecture, ![A]: ![N1, N2, X]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',N1),s('h4/type/num/num',N2)))) => s(A,'h4/const/list/EL'(s('h4/type/num/num',N1),s('h4/type/list/list'(A),'h4/const/rich_list/REPLICATE'(s('h4/type/num/num',N2),s(A,X))))) = s(A,X))).
