Nuprl Lemma : oal_nil_ident_l
∀a:LOSet. ∀b:AbDMon. ∀ps:|oal(a;b)|. ((00 ++ ps) = ps ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
oal_nil: 00,
oalist: oal(a;b),
all: ∀x:A. B[x],
equal: s = t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
oal_merge: ps ++ qs,
ycomb: Y,
ifthenelse: if b then t else f fi ,
null: null(as),
oal_nil: 00,
nil: [],
it: ⋅,
btrue: tt,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet
Lemmas referenced :
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
applyEquality,
lambdaEquality,
setElimination,
rename
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps:|oal(a;b)|. ((00 ++ ps) = ps)
Date html generated:
2016_05_16-AM-08_18_23
Last ObjectModification:
2015_12_28-PM-06_26_46
Theory : polynom_2
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