Nuprl Lemma : bar-converges_wf
∀[T:Type]. ∀[x:bar-base(T)]. ∀[a:T]. (x↓a ∈ ℙ)
Proof
Definitions occuring in Statement :
bar-converges: x↓a,
bar-base: bar-base(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bar-converges: x↓a,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_wf,
equal_wf,
unit_wf2,
bar-val_wf,
bar-base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
unionEquality,
hypothesisEquality,
inlEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:bar-base(T)]. \mforall{}[a:T]. (x\mdownarrow{}a \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_20_10
Last ObjectModification:
2015_12_26-PM-00_01_33
Theory : co-recursion
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