Nuprl Lemma : provisional-type_wf
∀[T:𝕌']. (Provisional(T) ∈ 𝕌')
Proof
Definitions occuring in Statement :
provisional-type: Provisional(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
provisional-type: Provisional(T),
prop: ℙ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
and: P ∧ Q,
pi1: fst(t),
implies: P ⇒ Q,
pi2: snd(t),
iff: P ⇐⇒ Q,
so_apply: x[s1;s2]
Lemmas referenced :
quotient_wf,
squash_wf,
iff_wf,
equal_wf,
uimplies_subtype,
provisional-equiv,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
productEquality,
universeEquality,
isectEquality,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
cumulativity,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
productElimination,
because_Cache,
functionEquality,
independent_isectElimination,
universeIsType,
independent_functionElimination,
productIsType,
isectIsType,
axiomEquality
Latex:
\mforall{}[T:\mBbbU{}']. (Provisional(T) \mmember{} \mBbbU{}')
Date html generated:
2020_05_20-AM-08_00_39
Last ObjectModification:
2020_05_17-PM-06_48_10
Theory : monads
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