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Theorem sorted-inc-left

a ≤ ar[n + 1] ⊦ sorted(ar, n + 1, m) → sorted(ar[n, a], n, m)

Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
Used by units in proved state: pair-insertion-sort, sort-invariants,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: sorted, less-eq-elem,
Used spec theorems:
- array/Put-other
Used simplifier rules:
- array/cngetput
- nat-basic/ref
- array/Size-put
- nat/succ-01
- nat/ler
- nat/lels
- nat/let
- nat/fle
- nat-basic/l-02
- nat-basic/a
- nat-basic/c
- array/cgetput
- nat-basic/f
- nat/lels-02