### 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

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