%   ORIGINAL: 'h4/thm/seq/SEQ_INV_'
% 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 x0. 'h4/const/seq/-->' x x0 /\ ~(x0 = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> 'h4/const/seq/-->' (\n. 'h4/const/realax/inv' (x n)) ('h4/const/realax/inv' x0)
%   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: !_0. (!x n. happ (happ _0 x) n = 'h4/const/realax/inv' (happ x n)) ==> (!x x0. 'h4/const/seq/-->' x x0 /\ ~(x0 = 'h4/const/real/real_of_num' 'h4/const/num/0') ==> 'h4/const/seq/-->' (happ _0 x) ('h4/const/realax/inv' x0))
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_3f64461,V_3f64457]: ![F, G]: (![X]: s(V_3f64457,happ(s(fun(V_3f64461,V_3f64457),F),s(V_3f64461,X))) = s(V_3f64457,happ(s(fun(V_3f64461,V_3f64457),G),s(V_3f64461,X))) => s(fun(V_3f64461,V_3f64457),F) = s(fun(V_3f64461,V_3f64457),G))).
fof('h4/thm/seq/SEQ_INV_', conjecture, ![V__0]: (![X, N]: s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun(fun('h4/type/num/num','h4/type/realax/real'),fun('h4/type/num/num','h4/type/realax/real')),V__0),s(fun('h4/type/num/num','h4/type/realax/real'),X))),s('h4/type/num/num',N))) = s('h4/type/realax/real','h4/const/realax/inv'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),X),s('h4/type/num/num',N))))) => ![X, X0]: ((p(s(bool,'h4/const/seq/-->'(s(fun('h4/type/num/num','h4/type/realax/real'),X),s('h4/type/realax/real',X0)))) & ~ (s('h4/type/realax/real',X0) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))))) => p(s(bool,'h4/const/seq/-->'(s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun(fun('h4/type/num/num','h4/type/realax/real'),fun('h4/type/num/num','h4/type/realax/real')),V__0),s(fun('h4/type/num/num','h4/type/realax/real'),X))),s('h4/type/realax/real','h4/const/realax/inv'(s('h4/type/realax/real',X0))))))))).
