Nuprl Lemma : has-value-implies-dec-isint

t,a,b:Base.  ((t)↓  ((t ∈ ℤ) ∨ (if is an integer then else b)))


Proof




Definitions occuring in Statement :  has-value: (a)↓ isint: isint def all: x:A. B[x] implies:  Q or: P ∨ Q member: t ∈ T int: base: Base sqequal: t
Definitions unfolded in proof :  all: x:A. B[x] implies:  Q has-value: (a)↓ member: t ∈ T uall: [x:A]. B[x] or: P ∨ Q top: Top guard: {T} prop:
Lemmas referenced :  base_wf equal-wf-base top_wf is-exception_wf has-value_wf_base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isintCases divergentSqle hypothesis cut lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed hypothesisEquality sqequalRule isintReduceTrue equalityTransitivity equalitySymmetry inlFormation because_Cache sqequalIntensionalEquality isect_memberFormation introduction sqequalAxiom isect_memberEquality voidElimination voidEquality inrFormation intEquality

Latex:
\mforall{}t,a,b:Base.    ((t)\mdownarrow{}  {}\mRightarrow{}  ((t  \mmember{}  \mBbbZ{})  \mvee{}  (if  t  is  an  integer  then  a  else  b  \msim{}  b)))



Date html generated: 2016_05_13-PM-03_22_49
Last ObjectModification: 2016_01_14-PM-06_46_37

Theory : call!by!value_1


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