Nuprl Lemma : mon_nat_op_wf

[g:IMonoid]. ∀[n:ℕ]. ∀[e:|g|].  (n ⋅ e ∈ |g|)


Proof




Definitions occuring in Statement :  mon_nat_op: n ⋅ e imon: IMonoid grp_car: |g| nat: uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  mon_nat_op: n ⋅ e uall: [x:A]. B[x] member: t ∈ T imon: IMonoid
Lemmas referenced :  nat_op_wf grp_car_wf nat_wf imon_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry setElimination rename isect_memberEquality because_Cache

Latex:
\mforall{}[g:IMonoid].  \mforall{}[n:\mBbbN{}].  \mforall{}[e:|g|].    (n  \mcdot{}  e  \mmember{}  |g|)



Date html generated: 2016_05_15-PM-00_16_26
Last ObjectModification: 2015_12_26-PM-11_39_43

Theory : groups_1


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