Nuprl Lemma : oal_lk_neg
∀s:LOSet. ∀g:AbDGrp. ∀ps:|oal(s;g)|. ((¬(ps = 00 ∈ |oal(s;g)|)) ⇒ (lk(--ps) = lk(ps) ∈ |s|))
Proof
Definitions occuring in Statement :
oal_lk: lk(ps),
oal_neg: --ps,
oal_nil: 00,
oalist: oal(a;b),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
equal: s = t ∈ T,
abdgrp: AbDGrp,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
abdgrp: AbDGrp,
abgrp: AbGrp,
grp: Group{i},
abdmonoid: AbDMon,
dmon: DMon,
uall: ∀[x:A]. B[x],
mon: Mon,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
guard: {T},
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
set_prod: s × t,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
oalist: oal(a;b),
dset_set: dset_set,
dset_list: s List,
dset_of_mon: g↓set,
oal_cons_pr: oal_cons_pr(x;y;ws),
oal_neg: --ps,
top: Top,
pi2: snd(t),
oal_lk: lk(ps)
Lemmas referenced :
oalist_cases_c,
subtype_rel_sets,
mon_wf,
inverse_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
grp_inv_wf,
comm_wf,
eqfun_p_wf,
grp_eq_wf,
sq_stable__comm,
not_wf,
equal_wf,
set_car_wf,
oalist_wf,
oal_nil_wf,
oal_lk_wf,
oal_neg_wf2,
abdgrp_wf,
loset_wf,
oal_neg_eq_nil,
istype-void,
oal_cons_pr_wf,
istype-assert,
before_wf,
map_wf,
set_prod_wf,
dset_of_mon_wf,
map_cons_lemma,
reduce_hd_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
isectElimination,
setEquality,
hypothesis,
cumulativity,
setElimination,
rename,
because_Cache,
lambdaEquality_alt,
setIsType,
universeIsType,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
functionEquality,
voidElimination,
equalityIstype,
productElimination,
functionIsType,
isect_memberEquality_alt
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDGrp. \mforall{}ps:|oal(s;g)|. ((\mneg{}(ps = 00)) {}\mRightarrow{} (lk(--ps) = lk(ps)))
Date html generated:
2019_10_16-PM-01_08_14
Last ObjectModification:
2018_11_27-AM-10_31_07
Theory : polynom_2
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