Nuprl Lemma : sq_stable__uimplies
∀[P,Q:ℙ]. (SqStable(Q) ⇒ SqStable(Q supposing P))
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Definitions unfolded in proof :
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
squash: ↓T,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
isect_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
thin,
imageElimination,
introduction,
independent_isectElimination,
imageMemberEquality,
hypothesisEquality,
baseClosed,
lemma_by_obid,
isectElimination,
lambdaEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (SqStable(Q) {}\mRightarrow{} SqStable(Q supposing P))
Date html generated:
2016_05_13-PM-03_09_45
Last ObjectModification:
2016_01_06-PM-05_49_13
Theory : core_2
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