Nuprl Lemma : usquash-implies-squash
∀[T:ℙ]. (usquash(T) ⇒ (↓T))
Proof
Definitions occuring in Statement :
usquash: usquash(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
usquash: usquash(T),
squash: ↓T,
prop: ℙ
Lemmas referenced :
squash_wf,
usquash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
pertypeElimination2,
sqequalRule,
thin,
imageElimination,
hypothesis,
imageMemberEquality,
hypothesisEquality,
baseClosed,
universeIsType,
extract_by_obid,
isectElimination,
lambdaEquality_alt,
dependent_functionElimination,
functionIsTypeImplies,
inhabitedIsType,
universeEquality
Latex:
\mforall{}[T:\mBbbP{}]. (usquash(T) {}\mRightarrow{} (\mdownarrow{}T))
Date html generated:
2020_05_19-PM-09_35_57
Last ObjectModification:
2020_05_17-PM-06_58_59
Theory : per!type!1
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