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Theorem append-to-le-01

⊦ m ≤ # x → ⌜x⌝ + σ to m = ⌜x to m⌝

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: append-to-ls, append-to-size-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 6
Used lemmas: append-cancel-l, to-succ-cons-l-lem, cons-append, to-succ-cons, append-finfin, to-zero-l, to-zero, append-assoc, empty-append, empty,
Used spec theorems:
- Used simplifier rules:
  - list-data/size-01
  - nat/lez-01
  - list/len-05
  - nat/lep-02
  - list/a
  - list/c
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/succ