%   ORIGINAL: 'h4/thm/arithmetic/num_case_cong_'
% 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: !'v\'' 'f\'' M 'M\'' v f. M = 'M\'' /\ ('M\'' = 'h4/const/num/0' ==> v = 'v\'') /\ (!n. 'M\'' = 'h4/const/num/SUC' n ==> f n = 'f\'' n) ==> 'h4/const/arithmetic/num_CASE' M v f = 'h4/const/arithmetic/num_CASE' 'M\'' 'v\'' 'f\''
%   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: !'v\'' 'f\'' M 'M\'' v f. M = 'M\'' /\ ('M\'' = 'h4/const/num/0' ==> v = 'v\'') /\ (!n. 'M\'' = 'h4/const/num/SUC' n ==> happ f n = happ 'f\'' n) ==> 'h4/const/arithmetic/num_CASE' M v f = 'h4/const/arithmetic/num_CASE' 'M\'' 'v\'' 'f\''
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_3f83166,V_3f83162]: ![F, G]: (![X]: s(V_3f83162,happ(s(fun(V_3f83166,V_3f83162),F),s(V_3f83166,X))) = s(V_3f83162,happ(s(fun(V_3f83166,V_3f83162),G),s(V_3f83166,X))) => s(fun(V_3f83166,V_3f83162),F) = s(fun(V_3f83166,V_3f83162),G))).
fof('h4/thm/arithmetic/num_case_cong_', conjecture, ![A]: ![V_27v_5c_27_27, V_27f_5c_27_27, M, V_27M_5c_27_27, V, F]: ((s('h4/type/num/num',M) = s('h4/type/num/num',V_27M_5c_27_27) & ((s('h4/type/num/num',V_27M_5c_27_27) = s('h4/type/num/num','h4/const/num/0') => s(A,V) = s(A,V_27v_5c_27_27)) & ![N]: (s('h4/type/num/num',V_27M_5c_27_27) = s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))) => s(A,happ(s(fun('h4/type/num/num',A),F),s('h4/type/num/num',N))) = s(A,happ(s(fun('h4/type/num/num',A),V_27f_5c_27_27),s('h4/type/num/num',N)))))) => s(A,'h4/const/arithmetic/num_CASE'(s('h4/type/num/num',M),s(A,V),s(fun('h4/type/num/num',A),F))) = s(A,'h4/const/arithmetic/num_CASE'(s('h4/type/num/num',V_27M_5c_27_27),s(A,V_27v_5c_27_27),s(fun('h4/type/num/num',A),V_27f_5c_27_27))))).
