Nuprl Lemma : isaxiom-append-nil
∀[l:Base]. (↑isaxiom(l)) supposing ((↑isaxiom(l @ [])) and (l @ [])↓)
Proof
Definitions occuring in Statement :
append: as @ bs,
nil: [],
has-value: (a)↓,
assert: ↑b,
bfalse: ff,
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
isaxiom: if z = Ax then a otherwise b,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
append: as @ bs,
list_ind: list_ind,
member: t ∈ T,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
cons: [a / b],
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
top: Top,
nil: [],
it: ⋅,
btrue: tt,
true: True,
not: ¬A,
prop: ℙ
Lemmas referenced :
has-value-implies-dec-ispair-2,
top_wf,
has-value-implies-dec-isaxiom-2,
bottom_diverge,
assert_wf,
has-value_wf_base,
is-exception_wf,
btrue_wf,
bfalse_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
sqequalHypSubstitution,
sqequalRule,
introduction,
cut,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
unionElimination,
voidElimination,
lambdaFormation,
isect_memberEquality,
voidEquality,
axiomEquality,
natural_numberEquality,
Error :universeIsType,
isectElimination,
isaxiomCases,
divergentSqle,
baseClosed,
baseApply,
closedConclusion,
axiomSqEquality,
Error :inhabitedIsType
Latex:
\mforall{}[l:Base]. (\muparrow{}isaxiom(l)) supposing ((\muparrow{}isaxiom(l @ [])) and (l @ [])\mdownarrow{})
Date html generated:
2019_06_20-PM-00_39_30
Last ObjectModification:
2018_09_26-PM-02_10_34
Theory : list_0
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