Nuprl Lemma : not_has-value_decidable_on_base
¬(∀t:Base. ((t)↓ ∨ (¬(t)↓)))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
base: Base
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
false: False,
has-value: (a)↓,
all: ∀x:A. B[x],
or: P ∨ Q
Lemmas referenced :
equal_wf,
not-id-sqle-bottom,
is-exception_wf,
exception-not-bottom,
bottom_diverge,
not_wf,
has-value_wf_base,
or_wf,
base_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
rename,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
hypothesisEquality,
sqleRule,
sqleReflexivity,
divergentSqle,
independent_functionElimination,
voidElimination,
baseClosed,
applyEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mneg{}(\mforall{}t:Base. ((t)\mdownarrow{} \mvee{} (\mneg{}(t)\mdownarrow{})))
Date html generated:
2016_05_13-PM-03_45_59
Last ObjectModification:
2016_01_14-PM-07_11_28
Theory : call!by!value_2
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