Nuprl Lemma : exception-not-value-or-bottom
∀[nm,val,t:Base]. (exception(nm; val) ≤ t) ⇒ False supposing ↓(t)↓ ∨ (t ~ ⊥)
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
false: False,
base: Base,
sqle: s ≤ t,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
false: False,
squash: ↓T,
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
exception-not-bottom_1,
exception-not-value_1,
base_wf,
has-value_wf_base,
or_wf,
squash_wf,
sqle_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
imageElimination,
unionElimination,
thin,
hypothesis,
lemma_by_obid,
isectElimination,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
sqequalIntensionalEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[nm,val,t:Base]. (exception(nm; val) \mleq{} t) {}\mRightarrow{} False supposing \mdownarrow{}(t)\mdownarrow{} \mvee{} (t \msim{} \mbot{})
Date html generated:
2016_05_13-PM-03_23_19
Last ObjectModification:
2016_01_14-PM-06_46_15
Theory : call!by!value_1
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