Nuprl Lemma : usquash-equality
∀[T:ℙ]. ∀[S:Type]. usquash(T) = usquash(S) ∈ Type supposing ↓T ⇐⇒ ↓S
Proof
Definitions occuring in Statement :
usquash: usquash(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
squash: ↓T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
usquash: usquash(T),
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
squash_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
sqequalRule,
productIsType,
functionIsType,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality,
pertypeEquality,
independent_functionElimination
Latex:
\mforall{}[T:\mBbbP{}]. \mforall{}[S:Type]. usquash(T) = usquash(S) supposing \mdownarrow{}T \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}S
Date html generated:
2020_05_19-PM-09_35_57
Last ObjectModification:
2020_05_17-PM-06_59_59
Theory : per!type!1
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