Nuprl Lemma : mset_fmon_wf
∀s:DSet. (mset_fmon(s) ∈ FAbMon(s))
Proof
Definitions occuring in Statement :
mset_fmon: mset_fmon(s),
free_abmonoid: FAbMon(S),
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
mset_fmon: mset_fmon(s),
free_abmonoid: FAbMon(S),
all: ∀x:A. B[x],
member: t ∈ T,
tlambda: λx:T. b[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
dset: DSet,
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x.t[x],
monoid_hom: MonHom(M1,M2),
so_apply: x[s],
unique_set: {!x:T | P[x]},
and: P ∧ Q,
cand: A c∧ B,
compose: f o g,
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
mset_mon: mset_mon{s},
grp_car: |g|,
pi1: fst(t),
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
grp_op: *,
pi2: snd(t),
grp_id: e,
infix_ap: x f y,
top: Top
Lemmas referenced :
mset_mon_wf,
mset_inj_wf,
set_car_wf,
grp_car_wf,
abmonoid_wf,
unique_set_wf,
monoid_hom_wf,
equal_wf,
compose_wf,
dset_wf,
squash_wf,
true_wf,
mset_for_mset_inj,
abmonoid_subtype_iabmonoid,
iff_weakening_equal,
mset_wf,
all_wf,
mset_for_wf,
mset_for_null_lemma,
monoid_hom_p_wf,
mset_for_mset_sum,
infix_ap_wf,
grp_op_wf,
grp_id_wf,
mset_for_functionality,
assert_wf,
mset_mem_wf,
dist_hom_over_mset_for,
mset_fact,
monoid_hom_properties
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
dependent_pairEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
applyEquality,
isectElimination,
setElimination,
rename,
functionEquality,
cumulativity,
universeEquality,
functionExtensionality,
productEquality,
dependent_set_memberEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
axiomEquality
Latex:
\mforall{}s:DSet. (mset\_fmon(s) \mmember{} FAbMon(s))
Date html generated:
2017_10_01-AM-09_59_37
Last ObjectModification:
2017_03_03-PM-01_00_44
Theory : mset
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