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:(Term Prop), tr:Term, L:(Term Prop). RepsTruth(L; Tr; tr) Prop | [RepsTruth_wf] |
Thm* P:(Term Prop), qP:Term, L:(Term Prop). ReflectsProp(P; qP; L) Prop | [ReflectsProp_wf] |
Thm* Tr,L:(Term Prop). 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] |