Nuprl Lemma : ideal_p_wf

[r:CRng]. ∀[a:|r| ⟶ ℙ].  (a Ideal of r ∈ ℙ)


Definitions occuring in Statement :  ideal_p: Ideal of R crng: CRng rng_car: |r| uall: [x:A]. B[x] prop: member: t ∈ T function: x:A ⟶ B[x]
Definitions unfolded in proof :  ideal_p: Ideal of R uall: [x:A]. B[x] member: t ∈ T prop: and: P ∧ Q crng: CRng rng: Rng add_grp_of_rng: r↓+gp grp_car: |g| pi1: fst(t) so_lambda: λ2x.t[x] implies:  Q subtype_rel: A ⊆B so_apply: x[s] infix_ap: y all: x:A. B[x]
Lemmas referenced :  subgrp_p_wf add_grp_of_rng_wf all_wf rng_car_wf infix_ap_wf rng_times_wf crng_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis because_Cache lambdaEquality functionEquality applyEquality universeEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity isect_memberEquality

\mforall{}[r:CRng].  \mforall{}[a:|r|  {}\mrightarrow{}  \mBbbP{}].    (a  Ideal  of  r  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-00_22_50
Last ObjectModification: 2015_12_27-AM-00_01_12

Theory : rings_1

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