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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