Nuprl Lemma : free-from-atom_wf_general
∀[T:Type]. ∀[x:T]. ∀[a:Atom$m]. (a#x:T ∈ ℙ)
Proof
Definitions occuring in Statement :
free-from-atom: a#x:T,
atom: Atom$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
Rules used in proof :
universeEquality,
hypothesisEquality,
Error :universeIsType,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
equalitySymmetry,
hypothesis,
equalityTransitivity,
axiomEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
freeFromAtomEquality,
atomnEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[a:Atom\$m]. (a\#x:T \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_20_18
Last ObjectModification:
2018_10_15-PM-10_13_42
Theory : atom_1
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