Nuprl Lemma : has-value-implies-dec-isatom2

`∀t,a,b:Base.  ((t)↓ `` ((t ∈ Atom2) ∨ (isatom2(t;a;b) ~ b)))`

Proof

Definitions occuring in Statement :  has-value: `(a)↓` atom: `Atom\$n` isatom2: `isatom2(z;a;b)` all: `∀x:A. B[x]` implies: `P `` Q` or: `P ∨ Q` member: `t ∈ T` 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 equal-wf-base top_wf is-exception_wf has-value_wf_base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isatom2Cases divergentSqle hypothesis cut lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed hypothesisEquality sqequalRule isAtom2ReduceTrue equalityTransitivity equalitySymmetry inlFormation because_Cache sqequalIntensionalEquality isect_memberFormation introduction sqequalAxiom isect_memberEquality voidElimination voidEquality inrFormation atomnEquality

Latex:
\mforall{}t,a,b:Base.    ((t)\mdownarrow{}  {}\mRightarrow{}  ((t  \mmember{}  Atom2)  \mvee{}  (isatom2(t;a;b)  \msim{}  b)))

Date html generated: 2016_05_13-PM-03_22_56
Last ObjectModification: 2016_01_14-PM-06_46_30

Theory : call!by!value_1

Home Index