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Theorem count-rec

⊦ i ≤ j → count-i2j(i, j) = i ' + count-i2j(i + 1, j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: count-i2j-length, count-i2j-max, count-i2j-min, count-i2j-ordered,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 13
Used lemmas: count-i2j-empty-02, counti2j-empty, counti2j-rec,
Used spec theorems:
- Used simplifier rules:
  - int-abs/elim-sub
  - int-abs/forward-le-01
  - int-basic2/ls
  - int-abs/lenls
  - int-abs/zero-gels-04
  - int-abs/lep
  - list/intlista/Nil
  - int-abs/sub-eq
  - int-abs/Sub-def
  - int-basic2/add-in
  - int-basic2/ls-01
  - int-abs/bet-01
  - list/intlista/app-04
  - int-abs/succ-02
  - int-abs/lels-01
  - oelem/intlista/irreflexivity
  - int-abs/le-add
  - list/intlista/app-03
  - list/intlista/a
  - list/intlista/Last
  - int-basic2/add-zero
  - int-abs/numsub
  - intnat/labs
  - int-abs/absle
  - int-abs/abssub
  - int-abs/sub-ls
  - int-abs/lels
  - int-basic2/add-c
  - int-abs/lep-01
  - int-basic2/add-a