Nuprl Lemma : concat-unroll
∀a:Top. (concat(a) ~ if a is a pair then (fst(a)) @ concat(snd(a)) otherwise if a = Ax then [] otherwise ⊥)
Proof
Definitions occuring in Statement :
concat: concat(ll),
append: as @ bs,
nil: [],
bottom: ⊥,
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,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
has-value: (a)↓,
member: t ∈ T,
implies: P ⇒ Q,
or: P ∨ Q,
pi1: fst(t),
pi2: snd(t),
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
is-exception_wf,
has-value_wf_base,
top_wf,
has-value-implies-dec-ispair-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
sqequalSqle,
cut,
sqleRule,
thin,
divergentSqle,
callbyvalueCallbyvalue,
sqequalHypSubstitution,
hypothesis,
callbyvalueReduce,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
unionElimination,
sqleReflexivity,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
introduction,
callbyvalueExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed,
isectElimination,
callbyvalueIspair,
ispairExceptionCases
Latex:
\mforall{}a:Top
(concat(a) \msim{} if a is a pair then (fst(a)) @ concat(snd(a))
otherwise if a = Ax then [] otherwise \mbot{})
Date html generated:
2016_05_14-AM-06_31_57
Last ObjectModification:
2016_01_14-PM-08_24_01
Theory : list_0
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