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Theorem countFun-in

⊦ i0 ∈ countFun(i, j, intfun) ↔ (∃ j0. i ≤ j0 ∧ j0 ≤ j ∧ intfun(j0) = i0)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: countFun-in-01, sum-countfun-not-ls,
Used by units in proved state: int-mod, int-fac,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 18
Used lemmas: countFun-base-01, countFun-rec, countFun-base,
Used spec theorems:
- Used simplifier rules:
  - int-abs/elim-sub
  - int-abs/forward-le-02
  - int-abs/lels-03
  - int-abs/forward-le-01
  - int-basic2/ls
  - int-abs/lenls
  - list/intlista/a
  - list/intlista/in-17
  - list/intlista/in-append
  - int-abs/sub-add-05
  - intnat/abs-pred
  - int-basic2/add-zero
  - list/intlista/in-empty
  - int-abs/succ-01
  - int-abs/ler
  - int-abs/forward-le-05
  - int-basic2/ls-02
  - int-abs/forward-lsle
  - int-abs/lels-01
  - int-basic1/ls-01
  - int-basic2/add-c
  - int-basic2/add-a
  - int-abs/zero-gels-04
  - int-abs/lep
  - int-abs/forward-lele
  - int-abs/lels
  - int-abs/anti