Nuprl Lemma : nat_op_mon_hom_1
∀[g:IMonoid]. ∀[a:|g|]. IsMonHom{<ℕ,+>,g}(λn.(n ⋅ a))
Proof
Definitions occuring in Statement :
nat_add_mon: <ℕ,+>
,
mon_nat_op: n ⋅ e
,
monoid_hom_p: IsMonHom{M1,M2}(f)
,
imon: IMonoid
,
grp_car: |g|
,
uall: ∀[x:A]. B[x]
,
lambda: λx.A[x]
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f)
,
fun_thru_2op: FunThru2op(A;B;opa;opb;f)
,
nat_add_mon: <ℕ,+>
,
grp_car: |g|
,
pi1: fst(t)
,
grp_op: *
,
pi2: snd(t)
,
grp_id: e
,
infix_ap: x f y
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
and: P ∧ Q
,
imon: IMonoid
Lemmas referenced :
mon_nat_op_add,
nat_wf,
mon_nat_op_zero,
grp_car_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
axiomEquality,
because_Cache,
productElimination,
independent_pairEquality,
setElimination,
rename
Latex:
\mforall{}[g:IMonoid]. \mforall{}[a:|g|]. IsMonHom\{<\mBbbN{},+>,g\}(\mlambda{}n.(n \mcdot{} a))
Date html generated:
2016_05_15-PM-00_18_03
Last ObjectModification:
2015_12_26-PM-11_38_31
Theory : groups_1
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