Nuprl Lemma : nat_op_mon_hom_2
∀[g:IAbMonoid]. ∀[n:ℕ]. IsMonHom{g,g}(λa.(n ⋅ a))
Proof
Definitions occuring in Statement :
mon_nat_op: n ⋅ e,
monoid_hom_p: IsMonHom{M1,M2}(f),
iabmonoid: IAbMonoid,
nat: ℕ,
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),
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
iabmonoid: IAbMonoid,
imon: IMonoid
Lemmas referenced :
mon_nat_op_op,
grp_car_wf,
mon_nat_op_id,
nat_wf,
iabmonoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
isect_memberEquality,
axiomEquality,
because_Cache,
productElimination,
independent_pairEquality
Latex:
\mforall{}[g:IAbMonoid]. \mforall{}[n:\mBbbN{}]. IsMonHom\{g,g\}(\mlambda{}a.(n \mcdot{} a))
Date html generated:
2016_05_15-PM-00_18_06
Last ObjectModification:
2015_12_26-PM-11_38_28
Theory : groups_1
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