Nuprl Lemma : lookup_oal_neg
∀a:DSet. ∀b:IGroup. ∀k:|a|. ∀ps:(|a| × |b|) List. (((--ps)[k]) = (~ (ps[k])) ∈ |b|)
Proof
Definitions occuring in Statement :
oal_neg: --ps,
lookup: as[k],
list: T List,
all: ∀x:A. B[x],
apply: f a,
product: x:A × B[x],
equal: s = t ∈ T,
igrp: IGroup,
grp_inv: ~,
grp_id: e,
grp_car: |g|,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
igrp: IGroup,
imon: IMonoid,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
oal_neg: --ps,
top: Top,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
pi1: fst(t),
pi2: snd(t),
infix_ap: x f y,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
not: ¬A
Lemmas referenced :
list_induction,
set_car_wf,
grp_car_wf,
equal_wf,
lookup_wf,
grp_id_wf,
oal_neg_wf,
grp_inv_wf,
list_wf,
map_nil_lemma,
lookup_nil_lemma,
igrp_wf,
dset_wf,
squash_wf,
true_wf,
grp_inv_id,
iff_weakening_equal,
map_cons_lemma,
lookup_cons_pr_lemma,
set_eq_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
assert_of_dset_eq,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
productEquality,
setElimination,
rename,
because_Cache,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
unionElimination,
equalityElimination,
independent_pairFormation,
impliesFunctionality
Latex:
\mforall{}a:DSet. \mforall{}b:IGroup. \mforall{}k:|a|. \mforall{}ps:(|a| \mtimes{} |b|) List. (((--ps)[k]) = (\msim{} (ps[k])))
Date html generated:
2017_10_01-AM-10_03_15
Last ObjectModification:
2017_03_03-PM-01_05_37
Theory : polynom_2
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