Nuprl Lemma : implies-usquash
∀[T:ℙ]. (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,
uimplies: b supposing a,
so_apply: x[s1;s2],
top: Top
Lemmas referenced :
top_wf,
pertype_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
thin,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality,
pointwiseFunctionalityForEquality,
isectElimination,
independent_isectElimination,
applyEquality,
isect_memberEquality,
voidElimination,
voidEquality,
pertypeMemberEquality
Latex:
\mforall{}[T:\mBbbP{}]. (T {}\mRightarrow{} (\mforall{}x:Top. (x \mmember{} usquash(T))))
Date html generated:
2019_06_20-AM-11_29_53
Last ObjectModification:
2018_09_05-PM-06_43_35
Theory : per!type!1
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