Nuprl Lemma : member-usquash
∀[T:ℙ]. (usquash(T) ⇒ (∀x:Top. (x ∈ usquash(T))))
Proof
Definitions occuring in Statement :
usquash: usquash(T),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
usquash: usquash(T),
prop: ℙ
Lemmas referenced :
istype-top,
usquash_wf,
implies-usquash
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
pertypeElimination2,
sqequalRule,
thin,
universeIsType,
hypothesisEquality,
hypothesis,
extract_by_obid,
isectElimination,
lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[T:\mBbbP{}]. (usquash(T) {}\mRightarrow{} (\mforall{}x:Top. (x \mmember{} usquash(T))))
Date html generated:
2020_05_19-PM-09_35_55
Last ObjectModification:
2020_05_17-PM-04_44_53
Theory : per!type!1
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