Nuprl Lemma : bottom_wf-partial
∀[A:Type]. ⊥ ∈ partial(A) supposing value-type(A)
Proof
Definitions occuring in Statement :
partial: partial(T),
bottom: ⊥,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
value-type_wf,
not-is-exception-bottom,
has-value_wf_base,
bottom_diverge,
base-member-partial
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
baseClosed,
independent_functionElimination,
voidElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mbot{} \mmember{} partial(A) supposing value-type(A)
Date html generated:
2016_05_14-AM-06_09_46
Last ObjectModification:
2016_01_06-PM-06_43_32
Theory : partial_1
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