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Proof step 6 from proof write-block-inv (previous step)

min(n1 - n0 + n2, VFS_PAGE_SIZE - (n0 + n2) % VFS_PAGE_SIZE) ≠ 0, write-inv(n0, n1, inode, buf, n2, dirs, files0, files1), n0 + n2 ≤ n1 ⊦ [vfs_writepage# (inode, (n0 + n2) / VFS_PAGE_SIZE, buf, n2, (n0 + n2) % VFS_PAGE_SIZE, min(n1 - n0 + n2, VFS_PAGE_SIZE - (n0 + n2) % VFS_PAGE_SIZE), dirs ; err, files1, asynced); n := min(n1 - n0 + n2, VFS_PAGE_SIZE - (n0 + n2) % VFS_PAGE_SIZE); if err = ESUCCESS then n2 := n2 + n] write-inv(n0, n1, inode, buf, n2, dirs, files0, files1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
VFS_PAGE_SIZE = n3 + (n0 + n2) % VFS_PAGE_SIZE, write-inv(n0, n1, inode, buf, n2, dirs, files0, files1), n0 + n2 ≤ n1, (n0 + n2) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [vfs_writepage#(inode, (n0 + n2) / VFS_PAGE_SIZE, buf, n2, (n0 + n2) % VFS_PAGE_SIZE, min(n1 - n0 + n2, n3), dirs; err, files1, asynced); n := min(n1 - n0 + n2, n3); if err = ESUCCESS then n2 := n2 + n] write-inv(n0, n1, inode, buf, n2, dirs, files0, files1), min(n1 - n0 + n2, n3) = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [(n0 + n2) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n3]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: (n0 + n2) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n3