Nuprl Lemma : ring_divs_wf
∀[r:RngSig]. ∀[p,q:|r|]. (p | q in r ∈ ℙ)
Proof
Definitions occuring in Statement :
ring_divs: a | b in r,
rng_car: |r|,
rng_sig: RngSig,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
ring_divs: a | b in r,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
exists_wf,
rng_car_wf,
equal_wf,
rng_times_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r:RngSig]. \mforall{}[p,q:|r|]. (p | q in r \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_22_14
Last ObjectModification:
2015_12_27-AM-00_01_29
Theory : rings_1
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