### Nuprl Lemma : decide-pair-if-has-value

`∀t:Base. ((t)↓ `` Dec(t ~ <fst(t), snd(t)>))`

Proof

Definitions occuring in Statement :  has-value: `(a)↓` decidable: `Dec(P)` pi1: `fst(t)` pi2: `snd(t)` all: `∀x:A. B[x]` implies: `P `` Q` pair: `<a, b>` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` has-value: `(a)↓` uall: `∀[x:A]. B[x]` pi1: `fst(t)` pi2: `snd(t)` decidable: `Dec(P)` or: `P ∨ Q` prop: `ℙ` top: `Top` not: `¬A` false: `False`
Lemmas referenced :  base_wf not_zero_sqequal_one top_wf not_wf is-exception_wf has-value_wf_base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation introduction ispairCases divergentSqle hypothesis cut lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed hypothesisEquality sqequalRule inlEquality sqequalAxiom sqequalIntensionalEquality baseApply closedConclusion isect_memberFormation isect_memberEquality because_Cache voidElimination voidEquality inrEquality lambdaEquality independent_functionElimination

Latex:
\mforall{}t:Base.  ((t)\mdownarrow{}  {}\mRightarrow{}  Dec(t  \msim{}  <fst(t),  snd(t)>))

Date html generated: 2016_05_13-PM-03_22_12
Last ObjectModification: 2016_01_14-PM-06_47_03

Theory : call!by!value_1

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