Nuprl Lemma : omral_dom_action
∀g:OCMon. ∀r:CDRng. ∀v:|r|. ∀ps:|omral(g;r)|. (↑(dom(v ⋅⋅ ps) ⊆b dom(ps)))
Proof
Definitions occuring in Statement :
omral_action: v ⋅⋅ ps,
omral_dom: dom(ps),
omralist: omral(g;r),
bsubmset: a ⊆b b,
assert: ↑b,
all: ∀x:A. B[x],
cdrng: CDRng,
rng_car: |r|,
oset_of_ocmon: g↓oset,
ocmon: OCMon,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
cdrng: CDRng,
crng: CRng,
rng: Rng,
omral_action: v ⋅⋅ ps,
rev_uimplies: rev_uimplies(P;Q),
ocmon: OCMon,
omon: OMon,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
infix_ap: x f y,
so_apply: x[s],
cand: A c∧ B,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
omralist: omral(g;r),
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
dset_list: s List,
set_prod: s × t,
add_grp_of_rng: r↓+gp,
grp_id: e,
pi2: snd(t),
grp_car: |g|,
finite_set: FiniteSet{s},
rev_bimplies: p ⇐b q,
bsupmset: a ⊇bs b,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
fset_map: fs-map(f, a),
squash: ↓T,
tidentity: Id{T},
identity: Id,
true: True
Lemmas referenced :
set_car_wf,
omralist_wf,
dset_wf,
rng_car_wf,
cdrng_wf,
ocmon_wf,
assert_functionality_wrt_bimplies,
bsubmset_wf,
oset_of_ocmon_wf,
subtype_rel_sets,
abmonoid_wf,
ulinorder_wf,
grp_car_wf,
assert_wf,
infix_ap_wf,
bool_wf,
grp_le_wf,
equal_wf,
grp_eq_wf,
eqtt_to_assert,
cancel_wf,
grp_op_wf,
uall_wf,
monot_wf,
fset_map_wf,
oset_of_ocmon_wf0,
grp_id_wf,
omral_dom_wf,
finite_set_wf,
omral_scale_wf,
bsubmset_functionality_wrt_bsubmset,
omral_dom_scale,
bsubmset_weakening,
mem_bsubmset,
mset_mem_wf,
assert_functionality_wrt_uiff,
fset_of_mset_wf,
mset_map_wf,
fset_of_mset_mem,
tidentity_wf,
squash_wf,
true_wf,
mset_wf,
mon_ident,
iabmonoid_subtype_imon,
abmonoid_subtype_iabmonoid,
abdmonoid_abmonoid,
ocmon_subtype_abdmonoid,
subtype_rel_transitivity,
abdmonoid_wf,
iabmonoid_wf,
imon_wf,
mset_map_id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
instantiate,
because_Cache,
productEquality,
cumulativity,
universeEquality,
functionEquality,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
setEquality,
independent_pairFormation,
imageElimination,
functionExtensionality,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}g:OCMon. \mforall{}r:CDRng. \mforall{}v:|r|. \mforall{}ps:|omral(g;r)|. (\muparrow{}(dom(v \mcdot{}\mcdot{} ps) \msubseteq{}\msubb{} dom(ps)))
Date html generated:
2017_10_01-AM-10_06_42
Last ObjectModification:
2017_03_03-PM-01_14_45
Theory : polynom_3
Home
Index