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Theorem isempty-append

⊦ isempty(buf0 + buf1) ↔ isempty(buf0) ∧ isempty(buf1)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 24
Used lemmas: isempty-elim-right0, isempty-ext, isempty,
Used spec theorems:
- array-splice/buffer/append-at
Used simplifier rules:
- nat-basic/eq-02
- nat/lep-02
- array-splice/buffer/append-len
- nat/le-def
- nat-basic/ref
- nat/ler
- nat-basic/add-base
- nat/lez
- array-splice/buffer/append-at1
- nat-basic/l-02
- nat/ls-le-simp
- array-splice/buffer/append-atp2
- array-splice/buffer/append-a
- nat-basic/l-01
- nat/fle-01
- nat/lels
- nat/elim-sub
- nat-basic/f
- nat-basic/l
- nat-basic/c
- nat-basic/a
- nat/lep