Nuprl Lemma : oal_inj_mon_hom
∀a:LOSet. ∀b:AbDMon. ∀k:|a|. IsMonHom{b,oal_mon(a;b)}(λv.inj(k,v))
Proof
Definitions occuring in Statement :
oal_inj: inj(k,v),
oal_mon: oal_mon(a;b),
all: ∀x:A. B[x],
lambda: λx.A[x],
monoid_hom_p: IsMonHom{M1,M2}(f),
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
oal_mon: oal_mon(a;b),
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
grp_id: e,
infix_ap: x f y,
all: ∀x:A. B[x],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
oal_nil: 00,
top: Top
Lemmas referenced :
grp_car_wf,
set_car_wf,
abdmonoid_wf,
loset_wf,
lookups_same_a,
oal_inj_wf,
grp_op_wf,
oal_merge_wf2,
equal_wf,
squash_wf,
true_wf,
lookup_oal_inj,
lookup_merge,
iff_weakening_equal,
mon_when_thru_op,
iabmonoid_subtype_imon,
abmonoid_subtype_iabmonoid,
abdmonoid_abmonoid,
subtype_rel_transitivity,
abmonoid_wf,
iabmonoid_wf,
imon_wf,
set_eq_wf,
infix_ap_wf,
mon_when_wf,
bool_wf,
grp_id_wf,
oal_nil_wf,
lookup_nil_lemma,
mon_when_of_id
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
dependent_functionElimination,
applyEquality,
independent_functionElimination,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
instantiate,
voidElimination,
voidEquality
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}k:|a|. IsMonHom\{b,oal\_mon(a;b)\}(\mlambda{}v.inj(k,v))
Date html generated:
2017_10_01-AM-10_04_43
Last ObjectModification:
2017_03_03-PM-01_07_54
Theory : polynom_2
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