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Proof step 200 from proof truncate-inv (previous step)

⟨afs_inode_sync#(mkinode(ino4, md, false, # links(ino4, dirs), 0, m0); dirs, files)⟩ (dirs = dirs0 ∧ files = files0), files1[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), files0[ino4] = mkfile(m, md0, m1, content1), files = files1 [ino4, mkfile (m0, md, # links(ino4, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m0 % VFS_PAGE_SIZE)] upto m0) ], m0 % VFS_PAGE_SIZE ≠ 0, files1 -- ino4 ≠ files0 -- ino4, afs-cons(dirs0, files0), afs-cons(dirs, files1), files1 ~ files0, ino4 ∈ files1, m0 / VFS_PAGE_SIZE ∈ content0 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 201:
⟨afs_inode_sync#(mkinode(ino4, md, false, # links(ino4, dirs), 0, m0); dirs, files)⟩ (dirs = dirs0 ∧ files = files0), VFS_PAGE_SIZE = n0 + m0 % VFS_PAGE_SIZE, files0[ino4] = mkfile(m, md0, m1, content1), files1[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), files = files1 [ino4, mkfile(m0, md, # links(ino4, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ], afs-cons(dirs, files1), afs-cons(dirs0, files0), files1 ~ files0, m0 / VFS_PAGE_SIZE ∈ content0, ino4 ∈ files1, m0 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ m0 % VFS_PAGE_SIZE = 0, files1 -- ino4 = files0 -- ino4

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m0 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n]

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: m0 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n