Nuprl Lemma : free-from-atom_wf
∀[T:Type]. ∀[x:T]. ∀[a:Atom1]. (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 :
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ
Rules used in proof :
universeEquality,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
atomnEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
freeFromAtomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[a:Atom1]. (a\#x:T \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_20_19
Last ObjectModification:
2018_10_15-PM-04_55_04
Theory : atom_1
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