Nuprl Lemma : decidable__squash
∀[p:ℙ]. (Dec(p) ⇒ Dec(↓p))
Proof
Definitions occuring in Statement :
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
decidable_wf,
sq_stable_from_decidable,
squash_elim,
squash_wf,
decidable_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache,
productElimination,
universeEquality
Latex:
\mforall{}[p:\mBbbP{}]. (Dec(p) {}\mRightarrow{} Dec(\mdownarrow{}p))
Date html generated:
2016_05_13-PM-03_16_17
Last ObjectModification:
2016_01_06-PM-05_21_19
Theory : core_2
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