Nuprl Lemma : oal_neg_sd_ordered
∀a:LOSet. ∀b:AbMon. ∀ps:(|a| × |b|) List. ((↑sd_ordered(map(λx.(fst(x));ps))) ⇒ (↑sd_ordered(map(λx.(fst(x));--ps))))
Proof
Definitions occuring in Statement :
oal_neg: --ps,
sd_ordered: sd_ordered(as),
map: map(f;as),
list: T List,
assert: ↑b,
pi1: fst(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
lambda: λx.A[x],
product: x:A × B[x],
abmonoid: AbMon,
grp_car: |g|,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
and: P ∧ Q,
uiff: uiff(P;Q),
guard: {T},
true: True,
prop: ℙ,
squash: ↓T,
uimplies: b supposing a,
pi1: fst(t),
mon: Mon,
abmonoid: AbMon,
dset: DSet,
qoset: QOSet,
poset: POSet{i},
loset: LOSet,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
assert_functionality_wrt_uiff,
sd_ordered_wf,
map_wf,
set_car_wf,
grp_car_wf,
oal_neg_wf,
squash_wf,
true_wf,
list_wf,
dset_wf,
oal_neg_keys_invar,
assert_wf,
abmonoid_wf,
loset_wf
Rules used in proof :
baseClosed,
imageMemberEquality,
natural_numberEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
applyEquality,
independent_isectElimination,
sqequalRule,
productElimination,
lambdaEquality,
because_Cache,
productEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
dependent_functionElimination,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:LOSet. \mforall{}b:AbMon. \mforall{}ps:(|a| \mtimes{} |b|) List.
((\muparrow{}sd\_ordered(map(\mlambda{}x.(fst(x));ps))) {}\mRightarrow{} (\muparrow{}sd\_ordered(map(\mlambda{}x.(fst(x));--ps))))
Date html generated:
2016_05_16-AM-08_19_06
Last ObjectModification:
2016_01_16-PM-11_57_14
Theory : polynom_2
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