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Theorem sum-red

⊦ (∀ n. n ∈ ns → f1(n) = f2(n)) → Σ(ns, f1) = Σ(ns, f2)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: distrmxmx-l, distrmxmx-r, distrmxmxvec, distrmxvecvec, distrvecmxmx, distrvevecmx, mult-assoc, multmx-column,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 11
Used lemmas: sum-rec, sum-base,
Used spec theorems:
- set-basic/natset/eq
Used simplifier rules:
- set-basic/natset/In-insert
- set-basic/natset/size-zero-01
- set-basic/natset/ne-01