Nuprl Lemma : squash-implies-usquash
∀[T:ℙ]. ((↓T) ⇒ usquash(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],
implies: P ⇒ Q,
squash: ↓T,
member: t ∈ T,
sq_stable: SqStable(P),
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable_usquash,
squash_wf,
implies-usquash
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
universeIsType,
universeEquality,
dependent_functionElimination,
Error :memTop
Latex:
\mforall{}[T:\mBbbP{}]. ((\mdownarrow{}T) {}\mRightarrow{} usquash(T))
Date html generated:
2020_05_19-PM-09_35_56
Last ObjectModification:
2020_05_17-PM-04_57_33
Theory : per!type!1
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