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Proof step 6 from proof isempty-empbuf (previous step)

⊦ (∀ n. n < # buf → buf[n] = empty) ↔ buf = mkempbuf(# buf)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 8:
⊦ (∀ n. n < # buf → buf[n] = empty) ↔ # buf = # mkempbuf(# buf) ∧ (∀ n. n < # buf → buf[n] = mkempbuf(# buf)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(# buf), buf] flags: <all paths>

Additional information

Used terms: mkempbuf(# buf), buf