Nuprl Lemma : sq_stable__subtype_rel
∀[A,B:Type]. SqStable(A ⊆r B)
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
squash: ↓T,
prop: ℙ
Lemmas referenced :
squash_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
hypothesisEquality,
applyEquality,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
dependent_functionElimination,
axiomEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. SqStable(A \msubseteq{}r B)
Date html generated:
2016_05_13-PM-03_18_38
Last ObjectModification:
2015_12_26-AM-09_08_24
Theory : subtype_0
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