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Theorem append-to-gr-01

⊦ # x < m → ⌜x⌝ + σ to m = ⌜x⌝ + (σ to (m - # x))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 10
Used lemmas: append-cancel-l, cons-to-num, append-finfin, append-assoc, empty-append, empty,
Used spec theorems:
- Used simplifier rules:
  - list-data/size-01
  - nat/sub-base
  - nat-basic2/succ
  - list/len-05
  - list/a
  - list/c
  - nat/elim-pred-c
  - nat-basic1/f
  - nat-basic2/l
  - nat/cancel-01
  - nat-basic2/oz
  - nat/elim-sub
  - nat/lels-03
  - nat-basic2/l-01
  - nat-basic2/a
  - nat-basic2/c
  - nat/eq-01