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Theorem split-prefix-append-to

⊦ # σ0 = ∞ → ((σ0 to n) + σ1 = σ0 ↔ σ1 = σ0 from n)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 10
Used lemmas:
Used spec theorems:
- stream/buffer-inf/extensionality
- stream/buffer-inf/get-from
- stream/buffer-inf/get-append-ls
Used simplifier rules:
- stream/buffer-inf/to-plus-from-simp
- stream/buffer-inf/inf-size-from
- nat-inf/less-inf2
- stream/buffer-inf/size-append
- nat-inf/disj
- nat-inf/addeqinf-cancel
- nat-inf/inf-less
- nat-inf/add-fin
- nat-basic/a
- nat-basic/c
- nat-inf/less-inf1
- stream/buffer-inf/size-to
- nat-inf/ls-natinf-to-nat-2-1
- nat-basic/l-02
- nat-inf/add-assoc
- nat-inf/add-comm
- stream/buffer-inf/get-append-notls
- nat-inf/sel
- nat/eq-01
- stream/buffer-inf/append-assoc