Nuprl Lemma : normalization-isaxiom
∀[a,b,c:Top]. (if a = Ax then b a otherwise c ~ if a = Ax then b Ax otherwise c)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
isaxiom: if z = Ax then a otherwise b,
apply: f a,
sqequal: s ~ t,
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
top: Top
Lemmas referenced :
is-exception_wf,
has-value_wf_base,
top_wf,
has-value-implies-dec-isaxiom-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueIsaxiom,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
unionElimination,
sqequalRule,
sqleReflexivity,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
isaxiomExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed,
isectElimination,
sqequalAxiom
Latex:
\mforall{}[a,b,c:Top]. (if a = Ax then b a otherwise c \msim{} if a = Ax then b Ax otherwise c)
Date html generated:
2016_05_13-PM-03_43_30
Last ObjectModification:
2016_01_14-PM-07_08_05
Theory : computation
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