Nuprl Lemma : oal_neg_wf2
∀a:LOSet. ∀b:AbDGrp. ∀ps:|oal(a;b)|. (--ps ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oal_neg: --ps,
oalist: oal(a;b),
all: ∀x:A. B[x],
member: t ∈ T,
abdgrp: AbDGrp,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
dset_list: s List,
set_prod: s × t,
dset_of_mon: g↓set,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
abdgrp: AbDGrp,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
top: Top,
dmon: DMon,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
true: True,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
grp_car: |g|,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
oal_neg_wf,
assert_functionality_wrt_uiff,
sd_ordered_wf,
map_wf,
set_car_wf,
grp_car_wf,
pi1_wf_top,
set_prod_wf,
dset_of_mon_wf,
eqfun_p_wf,
grp_eq_wf,
dset_wf,
squash_wf,
true_wf,
list_wf,
oal_neg_keys_invar,
assert_wf,
not_wf,
mem_wf,
grp_id_wf,
subtype_rel_self,
dset_of_mon_wf0,
pi2_wf,
oalist_wf,
abdgrp_wf,
loset_wf,
oal_neg_non_id_vals
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
sqequalRule,
setElimination,
thin,
rename,
dependent_set_memberEquality,
introduction,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
productElimination,
isectElimination,
productEquality,
because_Cache,
lambdaEquality,
independent_pairEquality,
isect_memberEquality,
voidElimination,
voidEquality,
applyEquality,
independent_isectElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_pairFormation,
independent_functionElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDGrp. \mforall{}ps:|oal(a;b)|. (--ps \mmember{} |oal(a;b)|)
Date html generated:
2018_05_22-AM-07_46_26
Last ObjectModification:
2018_05_19-AM-08_30_09
Theory : polynom_2
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