Nuprl Lemma : prod-if-ispair-append-nil
∀[l:Base]. (l ∈ Top × Top) supposing ((↑ispair(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]
,
top: Top
,
ispair: if z is a pair then a otherwise b
,
member: t ∈ T
,
product: x:A × B[x]
,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
uimplies: b supposing a
,
member: t ∈ T
,
append: as @ bs
,
list_ind: list_ind,
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
,
btrue: tt
,
top: Top
,
nil: []
,
it: ⋅
,
bfalse: ff
,
false: False
,
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,
cut,
sqequalHypSubstitution,
sqequalRule,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
unionElimination,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
Error :universeIsType,
isectElimination,
ispairCases,
divergentSqle,
baseClosed,
baseApply,
closedConclusion,
axiomSqEquality,
Error :inhabitedIsType
Latex:
\mforall{}[l:Base]. (l \mmember{} Top \mtimes{} Top) supposing ((\muparrow{}ispair(l @ [])) and (l @ [])\mdownarrow{})
Date html generated:
2019_06_20-PM-00_39_22
Last ObjectModification:
2018_09_26-PM-02_09_51
Theory : list_0
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