Nuprl Lemma : subst-term_wf

∀[opr:Type]. ∀[t:term(opr)]. ∀[s:(varname() × term(opr)) List].  (subst-term(s;t) ∈ term(opr))


Proof




Definitions occuring in Statement :  subst-term: subst-term(s;t),  term: term(opr),  varname: varname(),  list: T List,  uall: ∀[x:A]. B[x],  member: t ∈ T,  product: x:A × B[x],  universe: Type
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  subst-term: subst-term(s;t),  subtype_rel: A ⊆r B
Lemmas referenced :  replace-vars_wf,  subst-frame_wf,  list_wf,  varname_wf,  term_wf,  istype-universe
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  introduction,  cut,  sqequalRule,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  hypothesis,  applyEquality,  lambdaEquality_alt,  setElimination,  rename,  inhabitedIsType,  equalityTransitivity,  equalitySymmetry,  axiomEquality,  universeIsType,  productEquality,  isect_memberEquality_alt,  isectIsTypeImplies,  instantiate,  universeEquality

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



Date html generated: 2020_05_19-PM-09_57_56
Last ObjectModification: 2020_03_09-PM-04_10_07

Theory : terms


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