Nuprl Lemma : mon_nat_op_wf2
∀[g:IMonoid]. ∀[n:|(<ℤ+>↓hgrp)|]. ∀[e:|g|]. (n ⋅ e ∈ |g|)
Proof
Definitions occuring in Statement :
int_add_grp: <ℤ+>,
mon_nat_op: n ⋅ e,
hgrp_of_ocgrp: g↓hgrp,
imon: IMonoid,
grp_car: |g|,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
imon: IMonoid
Lemmas referenced :
mon_nat_op_wf,
grp_car_subtype,
grp_car_wf,
hgrp_of_ocgrp_wf,
int_add_grp_wf2,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g:IMonoid]. \mforall{}[n:|(<\mBbbZ{}+>\mdownarrow{}hgrp)|]. \mforall{}[e:|g|]. (n \mcdot{} e \mmember{} |g|)
Date html generated:
2018_05_21-PM-03_14_30
Last ObjectModification:
2018_05_19-AM-08_26_34
Theory : groups_1
Home
Index