ElisTarskiPf A Sections NuprlLIB Doc

Def x:A. B(x) == x:AB(x)

is mentioned by

Thm* (P P) False[prop_iff_contra]
Thm* (A B) (B C) (A C)[prop_iff_trans]
Thm* B (A B & C) (A C)[prop_and_iff]
Thm* Tr:(TermProp), tr:Term, L:(TermProp). RepsTruth(L; Tr; tr) Prop[RepsTruth_wf]
Thm* P:(TermProp), qP:Term, L:(TermProp). ReflectsProp(P; qP; L) Prop[ReflectsProp_wf]
Thm* Tr,L:(TermProp). RespectsNot(Tr; L) Prop[RespectsNot_wf]
Thm* t:Term. s(t) = SUBX(t; s(t))[s_reps]
Thm* t:Term. s(t) = SUBX(t; SUBX(f(t); f(t)))[s2]
Thm* t:Term. s(t) = SUBX(t; SUBX(f(t); UP(f(t))))[s1]
Thm* t:Term. s(t) Term[s_wf]
Thm* t:Term. f(t) Term[f_wf]
Thm* t,e:Term. SUBX(NOT(t); e) = NOT(SUBX(t; e))[qnot_subx]
Thm* t,r,t',r':Term. t = t' & r = r' SUBX(t; r) = SUBX(t'; r')[qsubx_repst]
Thm* t,r:Term. SUBX(t; r) Term[subx_wf]
Thm* t:Term. UP(t) = t[qup_up_repst]
Thm* t:Term. closed(t)[up_term_closed]
Thm* t:Term. closed(t) Prop[term_closed_wf]
Thm* t:Term. t = t[up_repst]
Thm* t:Term. t = t[up_reps]
Thm* t,x:Term. (t = x) Prop[repst_wf]
Thm* t,x:Term. (t = x) Prop[reps_wf2]
Thm* t:(u Term), x:u. (t = x) Prop[reps_wf]
Thm* (A Term) Type[termof_wf]
Def RepsTruth(L; Tr; tr) == (S:Term. (t:Term. S = t) L(SUBX(tr; S))) & RespectsNot(Tr; L) & ReflectsProp(Tr; tr; Tr)[RepsTruth]
Def ReflectsProp(P; qP; Tr) == t,qt:Term. qt = t {Tr(SUBX(qP; qt)) Tr(t)}[ReflectsProp]
Def RespectsNot(Tr; L) == t:Term. Tr(NOT(t)) L(t) & Tr(t)[RespectsNot]
Def closed(t) == s,v:Term. t[s/v] = t[term_closed]

In prior sections: core


ElisTarskiPf A Sections NuprlLIB Doc