Nuprl Lemma : uiff_weakening
∀[P:ℙ]. (SqStable(P) ⇒ {uiff(P;P)})
Proof
Definitions occuring in Statement :
sq_stable: SqStable(P),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
sq_stable: SqStable(P),
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
sq_stable_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
thin,
introduction,
imageMemberEquality,
hypothesisEquality,
baseClosed,
imageElimination,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
because_Cache,
lemma_by_obid,
isectElimination,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. (SqStable(P) {}\mRightarrow{} \{uiff(P;P)\})
Date html generated:
2016_05_13-PM-03_10_10
Last ObjectModification:
2016_01_06-PM-05_48_01
Theory : core_2
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