Nuprl Lemma : respects-equality-oalist1
∀[s:LOSet]. ∀[g:AbDMon]. respects-equality(|(s × (g↓set))| List;|oal(s;g)|)
Proof
Definitions occuring in Statement :
oalist: oal(a;b),
list: T List,
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
dset_of_mon: g↓set,
abdmonoid: AbDMon,
set_prod: s × t,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
abdmonoid: AbDMon,
subtype_rel: A ⊆r B,
dset: DSet,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
oalist: oal(a;b),
set_car: |p|,
dset_of_mon: g↓set,
set_prod: s × t,
pi1: fst(t),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
dset_list: s List,
set_eq: =b,
pi2: snd(t),
dmon: DMon,
poset_sig: PosetSig,
mon: Mon,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
grp_car: |g|,
grp_eq: =b,
so_apply: x[s]
Lemmas referenced :
sq_stable__respects-equality,
list_wf,
set_car_wf,
set_prod_wf,
dset_of_mon_wf,
oalist_wf,
abdmonoid_wf,
loset_wf,
abdmonoid_properties,
dmon_properties,
respects-equality-set-trivial,
loset_properties,
poset_properties,
grp_car_wf,
assert_wf,
sd_ordered_wf,
map_wf,
not_wf,
mem_wf,
bool_wf,
eqfun_p_wf,
set_eq_wf,
grp_id_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
dependent_functionElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
universeIsType,
productEquality,
spreadEquality,
because_Cache,
productElimination,
productIsType,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
functionIsType
Latex:
\mforall{}[s:LOSet]. \mforall{}[g:AbDMon]. respects-equality(|(s \mtimes{} (g\mdownarrow{}set))| List;|oal(s;g)|)
Date html generated:
2019_10_16-PM-01_07_02
Last ObjectModification:
2018_11_27-AM-11_21_56
Theory : polynom_2
Home
Index