Nuprl Lemma : ispair-or-isaxiom-append-nil
∀l:Base. ((l @ [])↓ ⇒ ((↑ispair(l @ [])) ∨ (↑isaxiom(l @ []))))
Proof
Definitions occuring in Statement :
append: as @ bs,
nil: [],
has-value: (a)↓,
assert: ↑b,
bfalse: ff,
btrue: tt,
ispair: if z is a pair then a otherwise b,
isaxiom: if z = Ax then a otherwise b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
base: Base
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
or: P ∨ Q,
has-value: (a)↓,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
true: True,
prop: ℙ,
top: Top,
guard: {T},
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
append: as @ bs,
list_ind: list_ind,
cons: [a / b],
not: ¬A,
false: False,
nil: [],
it: ⋅
Lemmas referenced :
bottom_diverge,
assert_of_bnot,
bfalse_wf,
btrue_wf,
is-exception_wf,
sqeqff_to_assert,
base_wf,
has-value_wf_base,
has-value-implies-dec-isaxiom-2,
top_wf,
false_wf,
has-value-implies-dec-ispair-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_functionElimination,
hypothesis,
unionElimination,
inlFormation,
natural_numberEquality,
isect_memberEquality,
voidElimination,
voidEquality,
inrFormation,
because_Cache,
isectElimination,
isaxiomCases,
divergentSqle,
isect_memberFormation,
introduction,
sqequalAxiom,
productElimination,
independent_isectElimination,
ispairCases,
callbyvalueCallbyvalue,
callbyvalueReduce
Latex:
\mforall{}l:Base. ((l @ [])\mdownarrow{} {}\mRightarrow{} ((\muparrow{}ispair(l @ [])) \mvee{} (\muparrow{}isaxiom(l @ []))))
Date html generated:
2016_05_14-AM-06_31_23
Last ObjectModification:
2016_01_14-PM-08_24_56
Theory : list_0
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