Nuprl Lemma : oal_dom_merge
∀a:LOSet. ∀b:AbDMon. ∀ps,qs:|oal(a;b)|. (↑(dom(ps ++ qs) ⊆b (dom(ps) ⋃ dom(qs))))
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
oal_dom: dom(ps),
oalist: oal(a;b),
bsubmset: a ⊆b b,
mset_union: a ⋃ b,
assert: ↑b,
all: ∀x:A. B[x],
abdmonoid: AbDMon,
loset: LOSet,
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,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
oal_dom: dom(ps),
mset_mem: mset_mem,
mk_mset: mk_mset(as),
mem: a ∈b as,
bexists: bexists,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
so_lambda: λ2x.t[x],
so_apply: x[s],
infix_ap: x f y
Lemmas referenced :
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf,
mem_bsubmset,
oal_dom_wf2,
oal_merge_wf2,
mset_union_wf,
oal_dom_wf,
abdmonoid_abmonoid,
assert_wf,
mset_mem_wf,
oal_merge_wf,
assert_functionality_wrt_uiff,
bor_wf,
fset_mem_union,
assert_of_bor,
decidable__or,
decidable__assert,
not_over_or,
uiff_transitivity,
not_wf,
bexists_wf,
map_wf,
grp_car_wf,
infix_ap_wf,
bool_wf,
set_eq_wf,
bnot_wf,
ball_wf,
assert_of_bnot,
bnot_thru_exists,
set_prod_wf,
dset_of_mon_wf,
oal_merge_dom_pred
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
productElimination,
independent_functionElimination,
independent_isectElimination,
unionElimination,
voidElimination,
productEquality,
independent_pairFormation,
promote_hyp
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps,qs:|oal(a;b)|. (\muparrow{}(dom(ps ++ qs) \msubseteq{}\msubb{} (dom(ps) \mcup{} dom(qs))))
Date html generated:
2016_05_16-AM-08_18_05
Last ObjectModification:
2015_12_28-PM-06_27_42
Theory : polynom_2
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