Nuprl Lemma : bar-converges-not-diverges

`∀[T:Type]. ∀[x:bar-base(T)]. ∀[a:T].  (x↓a `` (¬x↑))`

Proof

Definitions occuring in Statement :  bar-diverges: `x↑` bar-converges: `x↓a` bar-base: `bar-base(T)` uall: `∀[x:A]. B[x]` not: `¬A` implies: `P `` Q` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` implies: `P `` Q` not: `¬A` false: `False` bar-converges: `x↓a` exists: `∃x:A. B[x]` bar-diverges: `x↑` all: `∀x:A. B[x]` assert: `↑b` ifthenelse: `if b then t else f fi ` isl: `isl(x)` btrue: `tt` true: `True` prop: `ℙ`
Lemmas referenced :  assert_wf isl_wf unit_wf2 bar-diverges_wf bar-converges_wf bar-base_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation thin sqequalHypSubstitution productElimination dependent_functionElimination hypothesisEquality independent_functionElimination hypothesis natural_numberEquality hyp_replacement equalitySymmetry Error :applyLambdaEquality,  extract_by_obid isectElimination cumulativity sqequalRule voidElimination lambdaEquality because_Cache isect_memberEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[x:bar-base(T)].  \mforall{}[a:T].    (x\mdownarrow{}a  {}\mRightarrow{}  (\mneg{}x\muparrow{}))

Date html generated: 2016_10_21-AM-09_47_26
Last ObjectModification: 2016_07_12-AM-05_07_32

Theory : co-recursion

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