Nuprl Lemma : sq_stable__allowed
∀[T:𝕌']. ∀[x:Provisional(T)]. SqStable(allowed(x))
Proof
Definitions occuring in Statement :
allowed: allowed(x),
provisional-type: Provisional(T),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
provisional-type: Provisional(T),
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
pi1: fst(t),
rev_implies: P ⇐ Q,
pi2: snd(t),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
respects-equality: respects-equality(S;T),
allowed: allowed(x)
Lemmas referenced :
allowed_wf,
uimplies_subtype,
pi1_wf,
istype-universe,
subtype-respects-equality,
squash_wf,
provisional-type_wf,
member-usquash
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
introduction,
sqequalHypSubstitution,
imageElimination,
cut,
pointwiseFunctionalityForEquality,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
hypothesis,
pertypeElimination,
promote_hyp,
productElimination,
productIsType,
equalityIstype,
universeIsType,
universeEquality,
isectIsType,
because_Cache,
sqequalBase,
equalitySymmetry,
functionIsType,
equalityTransitivity,
inhabitedIsType,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality_alt,
applyEquality,
instantiate,
lambdaEquality_alt,
cumulativity,
independent_isectElimination,
hyp_replacement,
dependent_set_memberEquality_alt,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
isectEquality,
Error :memTop
Latex:
\mforall{}[T:\mBbbU{}']. \mforall{}[x:Provisional(T)]. SqStable(allowed(x))
Date html generated:
2020_05_20-AM-08_00_53
Last ObjectModification:
2020_05_17-PM-06_31_55
Theory : monads
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