Nuprl Lemma : add_grp_of_rng_wf_a
∀[r:Rng]. (r↓+gp ∈ Group{i})
Proof
Definitions occuring in Statement :
add_grp_of_rng: r↓+gp,
rng: Rng,
grp: Group{i},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
add_grp_of_rng: r↓+gp,
rng: Rng,
uimplies: b supposing a
Lemmas referenced :
rng_wf,
rng_all_properties,
mk_grp,
rng_car_wf,
rng_eq_wf,
rng_le_wf,
rng_plus_wf,
rng_zero_wf,
rng_minus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
productElimination,
setElimination,
rename,
independent_isectElimination
Latex:
\mforall{}[r:Rng]. (r\mdownarrow{}+gp \mmember{} Group\{i\})
Date html generated:
2016_05_15-PM-00_21_12
Last ObjectModification:
2015_12_27-AM-00_02_22
Theory : rings_1
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