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
Home
Index