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Proof step 47 from proof readpage-prepost (previous step)

# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), n1 < VFS_PAGE_SIZE, F(files -- m0), afs-cons(dirs, files), m0 ∈ files ⊦ ⌜zeropage⌝ [n1] = (content.stream from n * VFS_PAGE_SIZE)[n1], n ∈ content

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ n < # buf → ⌜buf⌝ [n] = buf[n]
Proof step 49:
# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), n1 < VFS_PAGE_SIZE, n1 < # zeropage, F(files -- m0), afs-cons(dirs, files), m0 ∈ files ⊦ (zeropage)[n1] = (content.stream from n * VFS_PAGE_SIZE)[n1], n ∈ content

Rule argument

spec: buffer-inf-conv name: tostream-at seq: ⊦ n < # buf → ⌜buf⌝ [n] = buf[n] subst: [n, buf] → [n1, zeropage] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # zeropage = VFS_PAGE_SIZE; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: n1, zeropage