Nuprl Lemma : decide-isaxiom-if-has-value
∀t,a,b:Base. ((t)↓ ⇒ ((if t = Ax then a otherwise b ~ a) ∨ (if t = Ax then a otherwise b ~ b)))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
isaxiom: if z = Ax then a otherwise b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
top: Top,
guard: {T},
prop: ℙ
Lemmas referenced :
base_wf,
top_wf,
is-exception_wf,
has-value_wf_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isaxiomCases,
divergentSqle,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
hypothesisEquality,
sqequalRule,
inlFormation,
sqequalIntensionalEquality,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
inrFormation
Latex:
\mforall{}t,a,b:Base. ((t)\mdownarrow{} {}\mRightarrow{} ((if t = Ax then a otherwise b \msim{} a) \mvee{} (if t = Ax then a otherwise b \msim{} b)))
Date html generated:
2016_05_13-PM-03_22_24
Last ObjectModification:
2016_01_14-PM-06_47_18
Theory : call!by!value_1
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