Nuprl Lemma : sq_stable__has-value
∀[A:Type]. ∀[a:bar(A)]. SqStable((a)↓) supposing value-type(A)
Proof
Definitions occuring in Statement :
bar: bar(T),
value-type: value-type(T),
has-value: (a)↓,
sq_stable: SqStable(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
has-value: (a)↓,
implies: P ⇒ Q,
sq_stable: SqStable(P),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T
Lemmas referenced :
squash_wf,
has-value_wf-bar,
value-type_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
because_Cache,
isect_memberEquality,
independent_isectElimination,
isectElimination,
lemma_by_obid,
hypothesis,
axiomSqleEquality,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
lambdaFormation,
imageElimination
Latex:
\mforall{}[A:Type]. \mforall{}[a:bar(A)]. SqStable((a)\mdownarrow{}) supposing value-type(A)
Date html generated:
2020_05_20-AM-09_07_28
Last ObjectModification:
2020_01_24-PM-02_33_35
Theory : bar!type
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