### Nuprl Lemma : rng_when_wf

[r:Rng]. ∀[b:𝔹]. ∀[p:|r|].  (when b. p ∈ |r|)

Proof

Definitions occuring in Statement :  rng_when: rng_when rng: Rng rng_car: |r| bool: 𝔹 uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  rng_when: rng_when uall: [x:A]. B[x] member: t ∈ T subtype_rel: A ⊆B grp: Group{i} mon: Mon imon: IMonoid prop: add_grp_of_rng: r↓+gp grp_car: |g| pi1: fst(t) rng: Rng
Lemmas referenced :  mon_when_wf add_grp_of_rng_wf_a grp_sig_wf monoid_p_wf grp_car_wf grp_op_wf grp_id_wf inverse_wf grp_inv_wf add_grp_of_rng_wf rng_car_wf bool_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 setEquality cumulativity axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

Latex:
\mforall{}[r:Rng].  \mforall{}[b:\mBbbB{}].  \mforall{}[p:|r|].    (when  b.  p  \mmember{}  |r|)

Date html generated: 2016_05_15-PM-00_28_51
Last ObjectModification: 2015_12_26-PM-11_58_07

Theory : rings_1

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