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Theorem sum-union

⊦ Σ(ns1 ∪ ns2, f) = Σ(ns1, f) + Σ(ns2 \ ns1, f)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 11
Used lemmas: sum-rec, sum-base,
Used spec theorems:
- set-basic/natset/eq
Used simplifier rules:
- set-union/natset/une
- set-union/natset/una
- set-union/natset/unc
- set-union/natset/diff-e-01
- ring/addzero-r
- ring/addassoc
- ring/addcom
- set-union/natset/unadd
- set-union/natset/diff-del-plus-2
- set-union/natset/unin-01
- set-union/natset/Difference
- set-basic/natset/size-zero-01
- set-basic/natset/ne-01
- set-union/natset/unin
- set-union/natset/diff-del-plus-1