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
Home
Index