Nuprl Lemma : sq_stable__strong-subtype
∀[A,B:Type]. SqStable(strong-subtype(A;B))
Proof
Definitions occuring in Statement :
strong-subtype: strong-subtype(A;B),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
strong-subtype_witness,
strong-subtype_wf,
squash_wf,
equal_wf,
exists_wf,
sq_stable__subtype_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_pairFormation,
setEquality,
lambdaEquality,
applyEquality,
because_Cache,
dependent_functionElimination,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. SqStable(strong-subtype(A;B))
Date html generated:
2016_05_13-PM-04_12_18
Last ObjectModification:
2016_01_14-PM-07_29_35
Theory : subtype_1
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