Nuprl Lemma : rng_nexp_unroll
∀[r:Rng]. ∀[n:ℕ+]. ∀[e:|r|]. ((e ↑r n) = ((e ↑r (n - 1)) * e) ∈ |r|)
Proof
Definitions occuring in Statement :
rng_nexp: e ↑r n,
rng: Rng,
rng_times: *,
rng_car: |r|,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
subtract: n - m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_nexp: e ↑r n,
mul_mon_of_rng: r↓xmn,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
rng: Rng
Lemmas referenced :
mon_nat_op_unroll,
mul_mon_of_rng_wf_c,
rng_car_wf,
nat_plus_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
axiomEquality,
setElimination,
rename
Latex:
\mforall{}[r:Rng]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[e:|r|]. ((e \muparrow{}r n) = ((e \muparrow{}r (n - 1)) * e))
Date html generated:
2016_05_15-PM-00_27_20
Last ObjectModification:
2015_12_26-PM-11_59_06
Theory : rings_1
Home
Index