Nuprl Lemma : ring_non_triv_wf
∀[r:Rng]. (r ≠ 0 ∈ ℙ)
Proof
Definitions occuring in Statement :
ring_non_triv: r ≠ 0,
rng: Rng,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
ring_non_triv: r ≠ 0,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng: Rng
Lemmas referenced :
nequal_wf,
rng_car_wf,
rng_one_wf,
rng_zero_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:Rng]. (r \mneq{} 0 \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_22_19
Last ObjectModification:
2015_12_27-AM-00_01_27
Theory : rings_1
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