Nuprl Lemma : fabmon_of_nat_mcp_wf
∀s:DSet. ∀m:MCopower(s;<ℤ+>↓hgrp). (fabmon_of_nat_mcp(m) ∈ FAbMon(s))
Proof
Definitions occuring in Statement :
fabmon_of_nat_mcp: fabmon_of_nat_mcp(m),
mcopower: MCopower(s;g),
free_abmonoid: FAbMon(S),
all: ∀x:A. B[x],
member: t ∈ T,
int_add_grp: <ℤ+>,
hgrp_of_ocgrp: g↓hgrp,
dset: DSet
Definitions unfolded in proof :
fabmon_of_nat_mcp: fabmon_of_nat_mcp(m),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
ocmon: OCMon,
mcopower: MCopower(s;g),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
dset: DSet,
guard: {T},
uimplies: b supposing a,
abmonoid: AbMon,
mon: Mon,
monoid_hom: MonHom(M1,M2),
compose: f o g,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
int_hgrp_el: zhgrp(n),
int_hgrp_to_nat: nat(n),
hgrp_of_ocgrp: g↓hgrp,
grp_car: |g|,
pi1: fst(t),
abgrp: AbGrp,
grp: Group{i},
imon: IMonoid,
hgrp_car: |g|+,
mon_nat_op: n ⋅ e,
nat_add_mon: <ℕ,+>,
grp_op: *,
pi2: snd(t),
grp_id: e,
int_add_grp: <ℤ+>
Lemmas referenced :
mk_fabmon,
mcopower_mon_wf,
hgrp_of_ocgrp_wf2,
int_add_grp_wf2,
ocmon_wf,
mcopower_inj_wf,
int_hgrp_el_wf,
false_wf,
le_wf,
set_car_wf,
mcopower_umap_wf,
mon_nat_op_wf2,
iabmonoid_subtype_imon,
abmonoid_subtype_iabmonoid,
subtype_rel_transitivity,
abmonoid_wf,
iabmonoid_wf,
imon_wf,
int_hgrp_to_nat_wf,
nat_subtype,
grp_car_wf,
hgrp_of_ocgrp_wf,
equal_wf,
compose_wf,
monoid_hom_p_wf,
mcopower_wf,
dset_wf,
mcopower_umap_is_hom,
zhgrp_op_mon_hom_1,
squash_wf,
true_wf,
mcopower_umap_comm_tri,
iff_weakening_equal,
mon_nat_op_one,
mcopower_umap_unique,
hgrp_car_wf,
int_add_grp_wf,
abgrp_wf,
grp_leq_wf,
grp_id_wf,
mon_nat_op_hom_swap,
abdmonoid_abmonoid,
ocmon_subtype_abdmonoid,
abdmonoid_wf,
mcopower_inj_is_hom,
nat_op_on_nat_add_mon,
mul-one
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
instantiate,
independent_isectElimination,
functionExtensionality,
functionEquality,
independent_functionElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination
Latex:
\mforall{}s:DSet. \mforall{}m:MCopower(s;<\mBbbZ{}+>\mdownarrow{}hgrp). (fabmon\_of\_nat\_mcp(m) \mmember{} FAbMon(s))
Date html generated:
2017_10_01-AM-10_01_18
Last ObjectModification:
2017_03_03-PM-01_04_01
Theory : polynom_1
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