Nuprl Lemma : comb_for_rng_sum_wf
λr,p,q,E,z. (Σ(r) p ≤ i < q. E[i]) ∈ r:Rng ⟶ p:ℤ ⟶ q:ℤ ⟶ E:({p..q-} ⟶ |r|) ⟶ (↓True) ⟶ |r|
Proof
Definitions occuring in Statement :
rng_sum: rng_sum,
rng: Rng,
rng_car: |r|,
int_seg: {i..j-},
so_apply: x[s],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rng: Rng
Lemmas referenced :
rng_sum_wf,
squash_wf,
true_wf,
int_seg_wf,
rng_car_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
setElimination,
rename,
intEquality
Latex:
\mlambda{}r,p,q,E,z. (\mSigma{}(r) p \mleq{} i < q. E[i]) \mmember{} r:Rng {}\mrightarrow{} p:\mBbbZ{} {}\mrightarrow{} q:\mBbbZ{} {}\mrightarrow{} E:(\{p..q\msupminus{}\} {}\mrightarrow{} |r|) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |r|
Date html generated:
2016_05_15-PM-00_22_04
Last ObjectModification:
2015_12_27-AM-00_01_35
Theory : rings_1
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