Nuprl Lemma : approx-per-trans
∀[T:Type]. Trans(Base;x,y.approx-per(T;x;y))
Proof
Definitions occuring in Statement :
approx-per: approx-per(T;x;y),
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
member: t ∈ T,
cand: A c∧ B,
exists: ∃x:A. B[x],
and: P ∧ Q,
approx-per: approx-per(T;x;y),
implies: P ⇒ Q,
all: ∀x:A. B[x],
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x]
Lemmas referenced :
base_wf,
approx-per_wf,
equal-wf-base,
sqle_wf_base
Rules used in proof :
universeEquality,
cumulativity,
because_Cache,
sqequalRule,
isectElimination,
extract_by_obid,
introduction,
productEquality,
equalitySymmetry,
equalityTransitivity,
hypothesis,
hypothesisEquality,
dependent_pairFormation,
cut,
independent_pairFormation,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}[T:Type]. Trans(Base;x,y.approx-per(T;x;y))
Date html generated:
2018_05_21-PM-00_04_24
Last ObjectModification:
2017_12_30-PM-02_02_16
Theory : rel_1
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