### Nuprl Lemma : rng_nexp_wf

`∀[r:Rng]. ∀[n:ℕ]. ∀[u:|r|].  (u ↑r n ∈ |r|)`

Proof

Definitions occuring in Statement :  rng_nexp: `e ↑r n` rng: `Rng` rng_car: `|r|` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  rng_nexp: `e ↑r n` uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` mul_mon_of_rng: `r↓xmn` grp_car: `|g|` pi1: `fst(t)` rng: `Rng`
Lemmas referenced :  mon_nat_op_wf2 mul_mon_of_rng_wf_c nat_subtype grp_car_wf mul_mon_of_rng_wf rng_car_wf nat_wf rng_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis applyEquality lambdaEquality setElimination rename axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

Latex:
\mforall{}[r:Rng].  \mforall{}[n:\mBbbN{}].  \mforall{}[u:|r|].    (u  \muparrow{}r  n  \mmember{}  |r|)

Date html generated: 2016_05_15-PM-00_26_38
Last ObjectModification: 2015_12_26-PM-11_59_32

Theory : rings_1

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