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Proof step 4 from proof zeropage-eq-fill (previous step)

# buf = VFS_PAGE_SIZE ⊦ fill(buf, zero) = mkzbuf(VFS_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 6:
⊦ VFS_PAGE_SIZE ≠ 0

Rule argument

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

Additional information

Used simplifier rules: page-size: ⊦ VFS_PAGE_SIZE ≠ 0;% ⊦ # fill(buf, d) = # buf; (s)% ⊦ # mkzbuf(n) = n; (s)% ⊦ n < # buf → fill(buf, d)[n] = d; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → mkzbuf(n)[m] = zero; (s) Used terms: mkzbuf(VFS_PAGE_SIZE), fill(buf, zero)