### Nuprl Lemma : isatom-implies-not-ispair

[t:Base]. (¬↑ispair(t)) supposing ((↑isatom(t)) and (t)↓)

Proof

Definitions occuring in Statement :  has-value: (a)↓ assert: b bfalse: ff btrue: tt uimplies: supposing a uall: [x:A]. B[x] isatom: if is an atom then otherwise b ispair: if is pair then otherwise b not: ¬A base: Base
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a not: ¬A implies:  Q false: False has-value: (a)↓ assert: b ifthenelse: if then else fi  btrue: tt bfalse: ff top: Top prop:
Lemmas referenced :  base_wf bfalse_wf btrue_wf assert_wf false_wf top_wf is-exception_wf has-value_wf_base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation thin ispairCases divergentSqle hypothesis lemma_by_obid sqequalHypSubstitution isectElimination baseClosed hypothesisEquality sqequalRule voidElimination sqequalAxiom isect_memberEquality because_Cache voidEquality independent_functionElimination lambdaEquality dependent_functionElimination isatomCases isatomReduceTrue equalityTransitivity equalitySymmetry

Latex:
\mforall{}[t:Base].  (\mneg{}\muparrow{}ispair(t))  supposing  ((\muparrow{}isatom(t))  and  (t)\mdownarrow{})

Date html generated: 2016_05_13-PM-03_28_09
Last ObjectModification: 2016_01_14-PM-06_43_51

Theory : call!by!value_1

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