Nuprl Lemma : per-value-property
∀[x:per-value()]. uand(x ∈ Base;(x)↓)
Proof
Definitions occuring in Statement :
per-value: per-value(),
uand: uand(A;B),
has-value: (a)↓,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uand: uand(A;B),
member: t ∈ T,
has-value: (a)↓,
subtype_rel: A ⊆r B,
per-value: per-value(),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
top: Top,
per-set: per-set(A;a.B[a]),
and: P ∧ Q,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
has-value_wf_base,
is-exception_wf,
subtype_rel-per-set,
base_wf,
istype-top,
istype-void,
sq_stable__has-value,
per-value_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
axiomSqleEquality,
hypothesis,
thin,
rename,
isaxiomCases,
divergentSqle,
extract_by_obid,
isectElimination,
baseClosed,
hypothesisEquality,
axiomEquality,
applyEquality,
Error :lambdaEquality_alt,
Error :universeIsType,
because_Cache,
axiomSqEquality,
Error :inhabitedIsType,
Error :isect_memberEquality_alt,
voidElimination,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
imageMemberEquality,
imageElimination,
Error :productIsType,
Error :equalityIsType4,
baseApply,
closedConclusion
Latex:
\mforall{}[x:per-value()]. uand(x \mmember{} Base;(x)\mdownarrow{})
Date html generated:
2019_06_20-AM-11_30_27
Last ObjectModification:
2018_10_07-AM-00_52_07
Theory : per!type
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