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Theorem sum-countFun-sub

⊦ 0 ≤ i → Σ countFun(i, j, intfun) - Σ countFun(i, j, intfun0) = Σ countFun(i, j, λ i0. intfun(i0) - intfun0(i0))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 18
Used lemmas: countFun-base-03, sum-one, sum-app, sum-empty, countFun-base, countFun-last,
Used spec theorems:
- Used simplifier rules:
  - int-abs/forward-le-01
  - int-abs/lels-01
  - int-abs/elim-sub
  - int-abs/numleledel-01
  - int-abs/forward-lele
  - int-abs/numle-02
  - int-abs/sub-eq
  - int-abs/sub-add-01
  - int-basic2/add-in
  - list/intlista/a
  - int-basic2/add-zero
  - int-abs/numsub
  - int-basic2/add-c
  - intnat/labs
  - int-abs/lels
  - int-abs/abs-le-succ
  - int-basic2/add-a
  - int-abs/mone-08
  - oelem/intlista/lel
  - int-abs/forward-lsle
  - int-abs/forward-le-02
  - int-abs/mone-06
  - int-abs/zero-gels-04
  - int-abs/anti