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Theorem ordered-precedes-h

⊦ ordered(ix0 + n0 ' + ix1 + n1 ' + ix2, x) → n1 < n0 ∧ ¬ x[n1] < x[n0]

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 24
Used lemmas: ordered-rec2,
Used spec theorems:
- Used simplifier rules:
  - list/indexseq/Nil
  - list/indexseq/c
  - nat/ax-02
  - nat/fle-01
  - nat/fle
  - nat-basic1/lf
  - oelem/indexseq/transitivity
  - oelem/nnn
  - nat-basic1/f
  - nat-basic1/ls-02
  - oelem/nll
  - nat-basic2/succ
  - nat/lels
  - list/indexseq/a
  - nat/le-ls-simp