Nuprl Lemma : sq_stable_iff_uimplies
∀[P:ℙ]. (SqStable(P) ⇐⇒ P supposing P)
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
squash_wf,
isect_wf,
sq_stable_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
universeEquality,
independent_functionElimination,
introduction,
imageMemberEquality,
baseClosed,
imageElimination,
rename,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[P:\mBbbP{}]. (SqStable(P) \mLeftarrow{}{}\mRightarrow{} P supposing P)
Date html generated:
2016_05_13-PM-03_10_33
Last ObjectModification:
2016_01_06-PM-05_48_12
Theory : core_2
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