Nuprl Lemma : allow_wf
∀[T:𝕌']. ∀[x:Provisional(T)]. allow(x) ∈ T supposing allowed(x)
Proof
Definitions occuring in Statement :
allow: allow(x),
allowed: allowed(x),
provisional-type: Provisional(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
provisional-type: Provisional(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
allow: allow(x),
allowed: allowed(x),
usquash: usquash(T),
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
pi1: fst(t),
prop: ℙ
Lemmas referenced :
allowed_wf,
provisional-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
hypothesis,
sqequalRule,
pertypeElimination,
promote_hyp,
thin,
productElimination,
pertypeElimination2,
independent_functionElimination,
universeIsType,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
lambdaFormation_alt,
hypothesisEquality,
equalityIstype,
dependent_functionElimination,
axiomEquality,
extract_by_obid,
isectElimination,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[x:Provisional(T)]. allow(x) \mmember{} T supposing allowed(x)
Date html generated:
2020_05_20-AM-08_00_58
Last ObjectModification:
2020_05_17-PM-06_35_07
Theory : monads
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