Nuprl Lemma : free-from-atom_wf2
∀[T:Type]. ∀[x:T]. ∀[a:Atom2]. (a#x:T ∈ ℙ)
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$n,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ
Lemmas referenced :
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
freeFromAtomEquality,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
atomnEquality,
Error :isect_memberEquality_alt,
isectElimination,
thin,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
instantiate,
extract_by_obid,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[a:Atom2]. (a\#x:T \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_20_21
Last ObjectModification:
2018_10_16-PM-01_50_49
Theory : atom_1
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