Nuprl Lemma : subst-frame-alpha

∀[opr:Type]. ∀t:term(opr). ∀s:(varname() × term(opr)) List.  alpha-eq-terms(opr;subst-frame(s;t);t)


Proof




Definitions occuring in Statement :  subst-frame: subst-frame(s;t),  alpha-eq-terms: alpha-eq-terms(opr;a;b),  term: term(opr),  varname: varname(),  list: T List,  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  product: x:A × B[x],  universe: Type
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  subst-frame: subst-frame(s;t),  member: t ∈ T,  subtype_rel: A ⊆r B,  prop: ℙ,  uimplies: b supposing a,  not: ¬A,  implies: P ⇒ Q,  false: False
Lemmas referenced :  alpha-avoid-equivalent,  vars-of-subst_wf,  subtype_rel_list,  varname_wf,  not_wf,  equal-wf-T-base,  nullvar_wf,  istype-void,  vars-of-subst-not-nullvar,  list_wf,  term_wf,  istype-universe
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  lambdaFormation_alt,  cut,  introduction,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  dependent_functionElimination,  hypothesis,  applyEquality,  setEquality,  baseClosed,  independent_isectElimination,  lambdaEquality_alt,  setElimination,  rename,  setIsType,  universeIsType,  because_Cache,  sqequalRule,  functionIsType,  equalityIstype,  productEquality,  instantiate,  universeEquality

Latex:
\mforall{}[opr:Type].  \mforall{}t:term(opr).  \mforall{}s:(varname()  \mtimes{}  term(opr))  List.    alpha-eq-terms(opr;subst-frame(s;t);t)



Date html generated: 2020_05_19-PM-09_57_50
Last ObjectModification: 2020_03_09-PM-04_10_03

Theory : terms


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