Nuprl Lemma : l-last-cons
∀[u,v:Top]. (l-last([u / v]) ~ if null(v) then u else l-last(v) fi )
Proof
Definitions occuring in Statement :
l-last: l-last(l),
null: null(as),
cons: [a / b],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
l-last: l-last(l),
null: null(as),
l-last-default: l-last-default(l;d),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
list_ind: list_ind,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
strictness-decide,
union-value-type,
value-type-has-value,
bottom-sqle,
has-value-implies-dec-isaxiom-2,
has-value-implies-dec-ispair-2,
has-value-ifthenelse-type,
top_wf,
strictness-apply,
lifting-strict-isaxiom,
lifting-strict-spread,
lifting-strict-ispair,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-callbyvalue,
list_ind_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
baseClosed,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueApply,
baseApply,
closedConclusion,
hypothesisEquality,
applyExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
because_Cache,
sqequalAxiom,
sqequalSqle,
divergentSqle,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry,
decideExceptionCases,
independent_functionElimination,
unionElimination,
sqleReflexivity,
rename,
unionEquality,
callbyvalueIspair,
ispairExceptionCases
Latex:
\mforall{}[u,v:Top]. (l-last([u / v]) \msim{} if null(v) then u else l-last(v) fi )
Date html generated:
2016_05_14-AM-07_42_01
Last ObjectModification:
2016_01_15-AM-08_42_16
Theory : list_1
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