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Theorem shortest-frag

frag*(IOAut(start, step, ext))(sl, al) ⊦ ∃ sl0, al0. sl0.head = sl.head ∧ sl0.last = sl.last ∧ frag*(IOAut(start, step, ext))(sl0, al0) ∧ (∀ sl1, al1. sl1.head = sl.head ∧ sl1.last = sl.last ∧ frag*(IOAut(start, step, ext))(sl1, al1) → # sl0 ≤ # sl1)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 16
Used lemmas: not-frag-empty,
Used spec theorems:
- Used simplifier rules:
  - list-data/l
  - nat-basic/f
  - nat/le-def
  - list-data/elim-add
  - list/c
  - nat/lels
  - nat-basic/c
  - nat-basic/a
  - nat-basic/s-04
  - list/a
  - nat-basic/succ
  - list/len-05
  - stream/append-finfin
  - list/e-01
  - list-data/size-nil
  - nat/lez
  - stream/empty
  - list-data/elim-list-c
  - list-last/l-02
  - nat/succ-01
  - nat-basic/l
  - nat/ls-le-simp
  - list/c-08