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Proof step 13 from proof write-loop-0 (previous step)

err = ESUCCESS, min(ino1 - ino2 + ino5, VFS_PAGE_SIZE - (ino2 + ino5) % VFS_PAGE_SIZE) ≠ 0, ino2 + ino5 ≤ ino1, ino5 = 0 → files = files1 ⊦ [vfs_writepage# (inode, (ino2 + ino5) / VFS_PAGE_SIZE, buf, ino5, (ino2 + ino5) % VFS_PAGE_SIZE, min(ino1 - ino2 + ino5, VFS_PAGE_SIZE - (ino2 + ino5) % VFS_PAGE_SIZE), dirs ; err, files, asynced); n := min(ino1 - ino2 + ino5, VFS_PAGE_SIZE - (ino2 + ino5) % VFS_PAGE_SIZE); if err = ESUCCESS then ino5 := ino5 + n] (ino5 = 0 → files = files1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
VFS_PAGE_SIZE = n0 + (ino2 + ino5) % VFS_PAGE_SIZE, err = ESUCCESS, ino2 + ino5 ≤ ino1, (ino2 + ino5) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE, ino5 = 0 → files = files1 ⊦ [vfs_writepage# (inode, (ino2 + ino5) / VFS_PAGE_SIZE, buf, ino5, (ino2 + ino5) % VFS_PAGE_SIZE, min(ino1 - ino2 + ino5, n0), dirs; err, files, asynced); n := min(ino1 - ino2 + ino5, n0); if err = ESUCCESS then ino5 := ino5 + n] (ino5 = 0 → files = files1), min(ino1 - ino2 + ino5, n0) = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [(ino2 + ino5) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n0]

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: (ino2 + ino5) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n0