Nuprl Lemma : no-value-bottom

`∀[T:Type]. ∀[x:partial(T)]. x ~ ⊥ supposing ¬(x)↓ supposing value-type(T)`

Proof

Definitions occuring in Statement :  partial: `partial(T)` bottom: `⊥` value-type: `value-type(T)` has-value: `(a)↓` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` not: `¬A` universe: `Type` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` prop: `ℙ`
Lemmas referenced :  no-value-bottom not_wf has-value_wf-partial partial_wf value-type_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis sqequalAxiom sqequalRule isect_memberEquality because_Cache equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[x:partial(T)].  x  \msim{}  \mbot{}  supposing  \mneg{}(x)\mdownarrow{}  supposing  value-type(T)

Date html generated: 2016_05_15-PM-10_04_09
Last ObjectModification: 2015_12_27-PM-05_16_59

Theory : bar!type

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