Nuprl Lemma : squash_functionality_wrt_implies
∀[P,Q:ℙ]. ({P ⇒ Q} ⇒ {(↓P) ⇒ (↓Q)})
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ
Lemmas referenced :
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
imageElimination,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
lemma_by_obid,
isectElimination,
functionEquality,
lambdaEquality,
dependent_functionElimination,
universeEquality,
isect_memberEquality,
because_Cache,
independent_functionElimination
Latex:
\mforall{}[P,Q:\mBbbP{}]. (\{P {}\mRightarrow{} Q\} {}\mRightarrow{} \{(\mdownarrow{}P) {}\mRightarrow{} (\mdownarrow{}Q)\})
Date html generated:
2016_05_13-PM-03_14_19
Last ObjectModification:
2016_01_06-PM-05_49_25
Theory : core_2
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