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Proof step 22 from proof read-inv-rec (previous step)

# 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), 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, min(n3, n2, n1) + n ≤ # buf1 ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((((content.stream from (n0 + n) / VFS_PAGE_SIZE * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from (n0 + n) % VFS_PAGE_SIZE) to min(n3, n2, n1)) + (⌜buf0⌝ from n + min(n3, n2, n1)) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# buf1 = n4 + n + min(n3, n2, n1), # buf0 = # buf1, n0 + n = m0 * VFS_PAGE_SIZE + n5, VFS_PAGE_SIZE = n2 + n5, files[ino] = mkfile(n1 + n0 + n, md, # links(ino, dirs), content), n5 < VFS_PAGE_SIZE, afs-cons(dirs, files), ino ∈ files, min(n3, n2, n1) + n ≤ # buf1, n3 + n ≤ # buf1, n + min(n3, n2, n1) ≤ # buf1, n5 + min(n3, n2, n1) ≤ VFS_PAGE_SIZE ⊦ (((content.stream from n0) to n) + (⌜buf0⌝ from n) to n) + ((((content.stream from m0 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE) from n5) to min(n3, n2, n1)) + (⌜buf0⌝ from n + min(n3, n2, n1)) = ((content.stream from n0) to min(n3, n2, n1) + n) + (⌜buf0⌝ from min(n3, n2, n1) + n), VFS_PAGE_SIZE = 0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [n0 + n, VFS_PAGE_SIZE, m, n5]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: n0 + n, VFS_PAGE_SIZE, m, n5