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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