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Proof step 10 from proof read-inv-rec (previous step)

# buf0 = # buf1, VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), ⌜buf1⌝ = ((content.stream from n0) to n) + (⌜buf0⌝ from n), afs-cons(dirs, files), ino ∈ files, n3 + n ≤ # buf1, n + min(n3, n2, n1) ≤ # buf1, (n0 + n) % VFS_PAGE_SIZE + min(n3, n2, n1) ≤ VFS_PAGE_SIZE ⊦ (⌜buf1⌝ to n) + ((⌜getpage((n0 + n) / VFS_PAGE_SIZE, content)⌝ from (n0 + n) % VFS_PAGE_SIZE) to min(n3, n2, n1)) + ((⌜buf1⌝ from n + min(n3, n2, n1)) to (# buf1 - n + min(n3, n2, n1))) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# buf0 = # buf1, # buf1 = n4 + n + min(n3, n2, n1), VFS_PAGE_SIZE = n2 + (n0 + n) % VFS_PAGE_SIZE, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), ⌜buf1⌝ = ((content.stream from n0) to n) + (⌜buf0⌝ from n), afs-cons(dirs, files), ino ∈ files, (n0 + n) % VFS_PAGE_SIZE + min(n3, n2, n1) ≤ VFS_PAGE_SIZE, n + min(n3, n2, n1) ≤ # buf1, n3 + n ≤ # buf1 ⊦ (⌜buf1⌝ to n) + ((⌜getpage((n0 + n) / VFS_PAGE_SIZE, content)⌝ from (n0 + n) % VFS_PAGE_SIZE) to min(n3, n2, n1)) + ((⌜buf1⌝ from n + min(n3, n2, n1)) to n4) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf1, n + min(n3, n2, n1), n4]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf1, n + min(n3, n2, n1), n4