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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