### Nuprl Lemma : has-value-implies-dec-ispair

`∀t,a,b:Base.  ((t)↓ `` ((t ~ <fst(t), snd(t)>) ∨ (if t is a pair then a otherwise b ~ b)))`

Proof

Definitions occuring in Statement :  has-value: `(a)↓` pi1: `fst(t)` pi2: `snd(t)` ispair: `if z is a pair then a otherwise b` all: `∀x:A. B[x]` implies: `P `` Q` or: `P ∨ Q` pair: `<a, b>` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` has-value: `(a)↓` member: `t ∈ T` uall: `∀[x:A]. B[x]` pi1: `fst(t)` pi2: `snd(t)` or: `P ∨ Q` top: `Top` guard: `{T}` prop: `ℙ`
Lemmas referenced :  base_wf top_wf is-exception_wf has-value_wf_base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation ispairCases divergentSqle hypothesis cut lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed hypothesisEquality sqequalRule inlFormation sqequalIntensionalEquality isect_memberFormation introduction sqequalAxiom isect_memberEquality because_Cache voidElimination voidEquality inrFormation baseApply closedConclusion

Latex:
\mforall{}t,a,b:Base.    ((t)\mdownarrow{}  {}\mRightarrow{}  ((t  \msim{}  <fst(t),  snd(t)>)  \mvee{}  (if  t  is  a  pair  then  a  otherwise  b  \msim{}  b)))

Date html generated: 2016_05_13-PM-03_22_34
Last ObjectModification: 2016_01_14-PM-06_46_49

Theory : call!by!value_1

Home Index