Nuprl Lemma : rng_sum_wf
∀[r:Rng]. ∀[p,q:ℤ]. ∀[E:{p..q-} ⟶ |r|]. (Σ(r) p ≤ i < q. E[i] ∈ |r|)
Proof
Definitions occuring in Statement :
rng_sum: rng_sum,
rng: Rng,
rng_car: |r|,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
rng_sum: rng_sum,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
grp: Group{i},
mon: Mon,
imon: IMonoid,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
rng: Rng
Lemmas referenced :
mon_itop_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,
rng_car_wf,
int_seg_wf,
add_grp_of_rng_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,
functionEquality,
isect_memberEquality,
because_Cache,
intEquality
Latex:
\mforall{}[r:Rng]. \mforall{}[p,q:\mBbbZ{}]. \mforall{}[E:\{p..q\msupminus{}\} {}\mrightarrow{} |r|]. (\mSigma{}(r) p \mleq{} i < q. E[i] \mmember{} |r|)
Date html generated:
2016_05_15-PM-00_22_02
Last ObjectModification:
2015_12_27-AM-00_01_46
Theory : rings_1
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