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Theorem indexWhere-length-notle

⊦ # x ≤ x.indexWhere(p) ↔ ¬ x.exists(p)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 8
Used lemmas: indexWhere-rec2, indexWhere-rec1, exists-rec, indexWhere-base, exists-base,
Used spec theorems:
- Used simplifier rules:
  - list-data/size-nil
  - list/a
  - list/c
  - nat-basic/c
  - nat-basic/a
  - nat/succ-01
  - nat-basic/succ
  - list/len-05
  - nat/lels
  - nat-basic/s-04
  - nat-basic/less-zero
  - nat-basic/f
  - list-data/l
  - nat/ls-le-simp