Nuprl Lemma : append-unroll
∀[as,bs:Top]. (as @ bs ~ if as is a pair then [fst(as) / ((snd(as)) @ bs)] otherwise if as = Ax then bs otherwise ⊥)
Proof
Definitions occuring in Statement :
append: as @ bs,
cons: [a / b],
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
ispair: if z is a pair then a otherwise b,
isaxiom: if z = Ax then a otherwise b,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
append: as @ bs,
list_ind: list_ind,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
cons: [a / b],
pi1: fst(t),
pi2: snd(t),
top: Top
Lemmas referenced :
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,
sqequalRule,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueCallbyvalue,
sqequalHypSubstitution,
hypothesis,
callbyvalueReduce,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
unionElimination,
sqleReflexivity,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
callbyvalueExceptionCases,
axiomSqleEquality,
exceptionSqequal,
callbyvalueIspair,
ispairExceptionCases,
sqequalAxiom
Latex:
\mforall{}[as,bs:Top].
(as @ bs \msim{} if as is a pair then [fst(as) / ((snd(as)) @ bs)]
otherwise if as = Ax then bs otherwise \mbot{})
Date html generated:
2016_05_14-AM-06_30_51
Last ObjectModification:
2016_01_14-PM-08_25_20
Theory : list_0
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