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Theorem range-dups

∀ i. i ∈ ints → 0 ≤ i ∧ i < j, 0 ≤ j, j < n→i(# ints) ⊦ dups(ints)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: This is one version of the pidgeon hole principle. The precondition 0 ≤ j implies that the list is not empty and could be replaced by the condition ints ≠ [].
Used by:
Used by units in proved state: int-mod,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 19
Used lemmas:
Used spec theorems:
- Used simplifier rules:
  - int-abs/anti
  - intnat/abs-pred
  - list/intlista/in-08
  - int-basic1/ls-01
  - int-abs/lels-01
  - int-abs/sub-ls
  - int-abs/leone
  - int-abs/sub-le-01
  - int-abs/sub-ls-01
  - int-abs/lels-03
  - nat-basic1/one
  - int-basic1/forward-pos
  - int-abs/succ-01
  - int-abs/ler
  - int-basic2/lst-03
  - int-abs/numadd-01
  - oelem/intlista/lel
  - int-abs/forward-le-01
  - oelem/intlista/transitivity
  - int-abs/les
  - int-abs/lels
  - list-del/intlista/dups
  - intnat/rax-04
  - nat-basic2/s
  - intnat/labs
  - int-abs/absle
  - oelem/intlista/irreflexivity
  - nat/pred-03
  - list-del/intlista/l
  - nat/elim-pred-c
  - nat-basic1/zero
  - intnat/num-n2i-ls-02
  - int-abs/forward-lele
  - list-del/intlista/in-01-01
  - int-basic2/ls-01
  - int-abs/succ-02
  - int-basic2/add-c
  - int-basic2/add-a
  - intnat/nat2int
  - int-abs/mone-06
  - int-abs/numls-02
  - intnat/n2i-add
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/one
  - int-abs/forward-le-05
  - list-data/intlista/l
  - list-del/intlista/dups-01
  - list-del/intlista/del1-in
  - int-abs/lels-02
  - int-abs/zero-gels-04