Nuprl Lemma : nat_op_wf
∀[g:IMonoid]. ∀[n:ℕ]. ∀[e:|g|].  (n x(*;e) e ∈ |g|)
Proof
Definitions occuring in Statement : 
nat_op: n x(op;id) e
, 
imon: IMonoid
, 
grp_id: e
, 
grp_op: *
, 
grp_car: |g|
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
nat_op: n x(op;id) e
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
imon: IMonoid
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
itop_wf, 
grp_car_wf, 
grp_op_wf, 
grp_id_wf, 
int_seg_wf, 
nat_wf, 
imon_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
setElimination, 
rename, 
hypothesisEquality, 
hypothesis, 
natural_numberEquality, 
lambdaEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[g:IMonoid].  \mforall{}[n:\mBbbN{}].  \mforall{}[e:|g|].    (n  x(*;e)  e  \mmember{}  |g|)
Date html generated:
2016_05_15-PM-00_15_13
Last ObjectModification:
2015_12_26-PM-11_40_35
Theory : groups_1
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