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Proof step 206 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files0 -- m = files -- m, files1 -- m = files -- m, files[m] = mkfile(m1, md, m3, content1), files0[m] = mkfile(m1, md, # links(m, dirs1), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs1), content0), buf-opt = none, err2 = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, m1 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, m0 ≤ m1, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ (content1.stream to m1).buf = splice(buf, 0, (content.stream to m1).buf, m0, m1 - m0), ino = 0, n1 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 207:
⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err2, dirs1, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err2 = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files0 -- m = files -- m, files1 -- m = files -- m, files[m] = mkfile(m1, md, m3, content1), files0[m] = mkfile(m1, md, # links(m, dirs1), content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs1), content0), buf-opt = none, err2 = ESUCCESS, content.stream from m1 = σ⊥, inode = mkinode(m, md, false, # links(m, dirs1), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs1), 0, m1), content0.stream to m1 = content.stream to m1, (content1.stream to m1).buf ≠ splice(buf, 0, (content.stream to m1).buf, m0, m1 - m0), ino ≠ 0, n1 ≠ 0, m1 < m0 + ino, afs-cons(dirs1, files1), of-cons(of1, dirs1, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, ino, dirs0, files0, files), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs1), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, m ∈ files1, m ∈ files, fd ∈ of1, n1 ≤ # buf, m0 ≤ m1, ⌊err0⌋ , err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat