Nuprl Lemma : decide-pair-if-has-value
∀t:Base. ((t)↓ ⇒ Dec(t ~ <fst(t), snd(t)>))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
decidable: Dec(P),
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
pair: <a, b>,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
has-value: (a)↓,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
top: Top,
not: ¬A,
false: False
Lemmas referenced :
base_wf,
not_zero_sqequal_one,
top_wf,
not_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
ispairCases,
divergentSqle,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
hypothesisEquality,
sqequalRule,
inlEquality,
sqequalAxiom,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
isect_memberFormation,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
inrEquality,
lambdaEquality,
independent_functionElimination
Latex:
\mforall{}t:Base. ((t)\mdownarrow{} {}\mRightarrow{} Dec(t \msim{} <fst(t), snd(t)>))
Date html generated:
2016_05_13-PM-03_22_12
Last ObjectModification:
2016_01_14-PM-06_47_03
Theory : call!by!value_1
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