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

`∀t,a,b:Base.  ((t)↓ `` ((t ~ λx.(t x)) ∨ (if t is lambda then a otherwise b ~ b)))`

Proof

Definitions occuring in Statement :  has-value: `(a)↓` islambda: `if z is lambda then a otherwise b` all: `∀x:A. B[x]` implies: `P `` Q` or: `P ∨ Q` apply: `f a` lambda: `λx.A[x]` 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]` 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 islambdaCases 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{}  \mlambda{}x.(t  x))  \mvee{}  (if  t  is  lambda  then  a  otherwise  b  \msim{}  b)))

Date html generated: 2016_05_13-PM-03_22_46
Last ObjectModification: 2016_01_14-PM-06_46_33

Theory : call!by!value_1

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