Nuprl Lemma : provision_wf
∀[T:𝕌']. ∀[ok:ℙ]. ∀[v:T supposing ok]. (provision(ok; v) ∈ Provisional(T))
Proof
Definitions occuring in Statement :
provision: provision(ok; v),
provisional-type: Provisional(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
provision: provision(ok; v),
provisional-type: Provisional(T),
uimplies: b supposing a,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
squash: ↓T,
cand: A c∧ B,
all: ∀x:A. B[x],
pi1: fst(t),
pi2: snd(t),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
istype-universe,
squash_wf,
iff_wf,
pi1_wf,
equal_wf,
pi2_wf,
uimplies_subtype,
provisional-equiv,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsType,
universeIsType,
hypothesisEquality,
isect_memberEquality_alt,
isectElimination,
thin,
isectIsTypeImplies,
inhabitedIsType,
universeEquality,
instantiate,
extract_by_obid,
productEquality,
isectEquality,
cumulativity,
lambdaEquality_alt,
functionEquality,
applyEquality,
productElimination,
independent_functionElimination,
because_Cache,
independent_isectElimination,
productIsType,
dependent_pairEquality_alt,
imageElimination,
independent_pairFormation,
lambdaFormation_alt,
independent_pairEquality,
equalityIstype,
dependent_functionElimination
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[ok:\mBbbP{}]. \mforall{}[v:T supposing ok]. (provision(ok; v) \mmember{} Provisional(T))
Date html generated:
2020_05_20-AM-08_00_45
Last ObjectModification:
2020_05_17-PM-11_02_51
Theory : monads
Home
Index