Nuprl Lemma : no-value-bottom-base
∀[x:Base]. x ~ ⊥ supposing (¬(x)↓) ∧ (¬is-exception(x))
Proof
Definitions occuring in Statement :
bottom: ⊥,
has-value: (a)↓,
is-exception: is-exception(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
top: Top,
prop: ℙ
Lemmas referenced :
has-value_wf_base,
is-exception_wf,
bottom-sqle,
and_wf,
not_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
divergentSqle,
sqequalHypSubstitution,
productElimination,
thin,
independent_functionElimination,
hypothesis,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
voidEquality,
sqequalAxiom,
sqequalRule,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:Base]. x \msim{} \mbot{} supposing (\mneg{}(x)\mdownarrow{}) \mwedge{} (\mneg{}is-exception(x))
Date html generated:
2016_05_15-PM-10_04_10
Last ObjectModification:
2015_12_27-PM-05_16_55
Theory : bar!type
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