Nuprl Lemma : has-value-l-last
∀[l:Base]. l ∈ Top × Top supposing (l-last(l))↓
Proof
Definitions occuring in Statement :
l-last: l-last(l),
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
product: x:A × B[x],
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l-last: l-last(l),
l-last-default: l-last-default(l;d),
list_ind: list_ind,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
top: Top,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
base_wf,
has-value_wf_base,
bottom_diverge,
has-value-implies-dec-isaxiom-2,
top_wf,
has-value-implies-dec-ispair-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
callbyvalueApply,
hypothesis,
callbyvalueCallbyvalue,
callbyvalueReduce,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
unionElimination,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
because_Cache
Latex:
\mforall{}[l:Base]. l \mmember{} Top \mtimes{} Top supposing (l-last(l))\mdownarrow{}
Date html generated:
2016_05_14-AM-07_41_47
Last ObjectModification:
2016_01_15-AM-08_35_46
Theory : list_1
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