Nuprl Lemma : allowed_wf
∀[T:𝕌']. ∀[x:Provisional(T)]. (allowed(x) ∈ ℙ)
Proof
Definitions occuring in Statement :
allowed: allowed(x),
provisional-type: Provisional(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
provisional-type: Provisional(T),
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
allowed: allowed(x),
iff: P ⇐⇒ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
pi1: fst(t),
rev_implies: P ⇐ Q,
pi2: snd(t),
subtype_rel: A ⊆r B,
squash: ↓T,
respects-equality: respects-equality(S;T)
Lemmas referenced :
squash_wf,
uimplies_subtype,
subtype-respects-equality,
provisional-type_wf,
istype-universe,
usquash-equality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
universeEquality,
hypothesis,
sqequalRule,
pertypeElimination,
promote_hyp,
thin,
productElimination,
productIsType,
equalityIstype,
universeIsType,
isectIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
sqequalBase,
equalitySymmetry,
functionIsType,
equalityTransitivity,
inhabitedIsType,
lambdaFormation_alt,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality_alt,
applyEquality,
instantiate,
cumulativity,
independent_isectElimination,
imageElimination,
hyp_replacement,
dependent_set_memberEquality_alt,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
lambdaEquality_alt,
isectEquality,
axiomEquality,
isectIsTypeImplies
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[x:Provisional(T)]. (allowed(x) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_00_51
Last ObjectModification:
2020_05_17-PM-07_17_30
Theory : monads
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