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Theorem array-le-trans

⊦ ar0 ≤ ar1 ∧ ar1 ≤ ar2 → ar0 ≤ ar2

Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss, forward, localforward,
Comment:
Used by: array-le-kill-prefix, array-le-refl, array-le-same-prefix, array-le-same-prepart, array-le-same-prepart2, array-neg-le-eq-2, next-perm-greaterPerms, next-perm-smallerPerms, next-proper-permutation,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 15
Used lemmas: lexicographic-rec1, lexicographic-base3, lexicographic-base2,
Used spec theorems:
- Used simplifier rules:
  - list/natarray-oarray-sort/c
  - list/natarray-oarray-sort/a
  - nat/lels-02
  - nat-basic/f
  - oelem/natarray/transitivity
  - nat-basic/lf
  - nat-basic/succ
  - oelem/natarray/lel
  - nat-basic/lf-01
  - nat-basic/l-05
  - nat-basic/a
  - nat-basic/c