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
Home
Index