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Theorem count-i2j-in

⊦ i0 ∈ count-i2j(i, j) ↔ i ≤ i0 ∧ i0 ≤ j

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: coprimes-max, coprimes-min, coprimes-prime, count-i2j-no-dups, 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: 15
Used lemmas: count-empty, counti2j-empty, counti2j-rec,
Used spec theorems:
- Used simplifier rules:
  - int-abs/zero-gels-01
  - int-abs/lels-03
  - int-abs/lep
  - list/intlista/a
  - list/intlista/in-17
  - list/intlista/in-append
  - list/intlista/Last
  - int-abs/forward-le-01
  - int-abs/lels
  - int-abs/absle
  - intnat/labs
  - int-basic2/add-in
  - int-abs/forward-lele
  - int-abs/abs-03
  - int-abs/numle-02
  - int-abs/succ-01
  - int-abs/absls-06
  - int-abs/mone-08
  - int-abs/forward-le-02
  - int-abs/minus-add
  - list/intlista/in-empty
  - int-basic2/add-zero
  - int-abs/anti
  - int-abs/elim-sub
  - int-abs/succ-02
  - int-abs/lels-02
  - int-abs/lep-01
  - int-basic2/add-a
  - int-basic2/add-c
  - int-abs/le-add
  - int-abs/ler
  - int-abs/lels-01
  - oelem/intlista/lel
  - int-basic2/ls
  - int-abs/lenls
  - int-abs/le-add-03