Nuprl Lemma : squash_thru_implies_dec
∀[P,Q:ℙ]. uiff(↓P ⇒ Q;P ⇒ (↓Q)) supposing Dec(P)
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
decidable_wf,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalHypSubstitution,
imageElimination,
independent_functionElimination,
thin,
hypothesis,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
lambdaEquality,
dependent_functionElimination,
lemma_by_obid,
isectElimination,
functionEquality,
unionElimination,
voidElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. uiff(\mdownarrow{}P {}\mRightarrow{} Q;P {}\mRightarrow{} (\mdownarrow{}Q)) supposing Dec(P)
Date html generated:
2016_05_13-PM-03_16_22
Last ObjectModification:
2016_01_06-PM-05_50_09
Theory : core_2
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