Nuprl Lemma : name-subst_wf
∀[s:(Name × Name) List]. ∀[x:Name]. (name-subst(s;x) ∈ Name)
Proof
Definitions occuring in Statement :
name-subst: name-subst(s;x),
name: Name,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-subst: name-subst(s;x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
apply-alist_wf,
name_wf,
name-deq_wf,
unit_wf2,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
unionEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
productEquality
Latex:
\mforall{}[s:(Name \mtimes{} Name) List]. \mforall{}[x:Name]. (name-subst(s;x) \mmember{} Name)
Date html generated:
2019_06_20-PM-01_58_10
Last ObjectModification:
2018_08_21-PM-01_55_31
Theory : decidable!equality
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