Nuprl Lemma : lifting-ispair-concat
∀[a,b,c:Top]. (concat(if a is a pair then b otherwise c) ~ if a is a pair then concat(b) otherwise concat(c))
Proof
Definitions occuring in Statement :
concat: concat(ll),
uall: ∀[x:A]. B[x],
top: Top,
ispair: if z is a pair then a otherwise b,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
top: Top,
uimplies: b supposing a
Lemmas referenced :
has-value-implies-dec-ispair,
concat-strict,
top_wf,
is-exception_wf,
has-value_wf_base,
has-value-implies-dec-ispair-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
sqequalHypSubstitution,
sqequalRule,
callbyvalueExceptionCases,
hypothesis,
axiomSqleEquality,
callbyvalueReduce,
callbyvalueIspair,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
unionElimination,
sqleReflexivity,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
ispairExceptionCases,
exceptionSqequal,
sqequalAxiom,
independent_isectElimination
Latex:
\mforall{}[a,b,c:Top].
(concat(if a is a pair then b otherwise c) \msim{} if a is a pair then concat(b) otherwise concat(c))
Date html generated:
2016_05_15-PM-02_07_25
Last ObjectModification:
2016_01_15-PM-10_24_12
Theory : untyped!computation
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