Nuprl Lemma : approx-per_wf
∀[T:Type]. ∀[x,y:Base]. (approx-per(T;x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
approx-per: approx-per(T;x;y),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
prop: ℙ,
approx-per: approx-per(T;x;y),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
all_wf,
equal-wf-base,
sqle_wf_base,
base_wf,
exists_wf
Rules used in proof :
universeEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionEquality,
because_Cache,
hypothesisEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:Base]. (approx-per(T;x;y) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-00_04_20
Last ObjectModification:
2017_12_30-PM-01_58_47
Theory : rel_1
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