Nuprl Lemma : squash_functionality_wrt_uiff
∀[P,Q:ℙ]. ({P ⇐⇒ Q} ⇒ {uiff(↓P;↓Q)})
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
imageElimination,
independent_functionElimination,
hypothesis,
imageMemberEquality,
hypothesisEquality,
baseClosed,
lemma_by_obid,
isectElimination,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache
Latex:
\mforall{}[P,Q:\mBbbP{}]. (\{P \mLeftarrow{}{}\mRightarrow{} Q\} {}\mRightarrow{} \{uiff(\mdownarrow{}P;\mdownarrow{}Q)\})
Date html generated:
2016_05_13-PM-03_14_26
Last ObjectModification:
2016_01_06-PM-05_49_35
Theory : core_2
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