Nuprl Lemma : provisional-type-wf2
∀[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],
equiv_rel: EquivRel(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
cand: A c∧ B,
rev_implies: P ⇐ Q,
sym: Sym(T;x,y.E[x; y]),
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
respects-equality: respects-equality(S;T),
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
quotient_wf,
squash_wf,
iff_wf,
equal_wf,
uimplies_subtype,
istype-universe,
pi1_wf,
pi2_wf,
subtype-respects-equality
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,
independent_pairFormation,
lambdaFormation_alt,
imageElimination,
imageMemberEquality,
baseClosed,
functionIsType,
equalityIstype,
isect_memberEquality_alt,
dependent_functionElimination
Latex:
\mforall{}[T:\mBbbU{}'']. (Provisional(T) \mmember{} \mBbbU{}'')
Date html generated:
2020_05_20-AM-08_01_13
Last ObjectModification:
2020_05_17-PM-08_04_25
Theory : monads
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