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Theorem sum-countfun-not-ls

∃ i1, j1. i0 ≤ i1 ∧ i1 ≤ j0 ∧ intfun(i1) = i ∧ i0 ≤ j1 ∧ j1 ≤ j0 ∧ intfun(j1) = j ∧ i1 ≠ j1, ∀ i1. i0 ≤ i1 ∧ i1 ≤ j0 → 0 ≤ intfun(i1), 0 ≤ i0 ⊦ ¬ Σ countFun(i0, j0, intfun) < i + j

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: 14
Proof steps: 32
Used lemmas: countFun-in, countFun-in-01, sum-in-not-ls, sum-one, sum-app, countFun-last,
Used spec theorems:
- Used simplifier rules:
  - list/intlista/a
  - intnat/abs-pred
  - oelem/intlista/irreflexivity
  - oelem/intlista/transitivity
  - int-abs/forward-le-01
  - int-abs/succ-01
  - int-abs/sub-le-01
  - int-basic1/ls-01
  - int-basic2/ls-01
  - int-abs/zero-gels-04
  - int-abs/anti
  - int-abs/lels-02
  - int-abs/forward-le-05
  - int-abs/forward-lels
  - int-abs/forward-lele
  - int-abs/lels-01
  - int-abs/zero-gels-01
  - int-abs/forward-le-02
  - int-basic2/add-c
  - int-basic2/add-a
  - int-basic2/ls
  - int-abs/forward-lsle
  - int-abs/lels
  - int-abs/ler
  - int-abs/lels-03