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Proof step 27 from proof truncate-inv (previous step)

⟨afs_truncate_internal#(n, pageno; inode, buf-opt, ino0, ino, isdir, err, dirs, files; asynced)⟩ ( inode = inode1 ∧ buf-opt = buf-opt1 ∧ ino0 = ino2 ∧ ino = ino3 ∧ (isdir ↔ isdir0) ∧ err = err1 ∧ dirs = dirs1 ∧ files = files2 ∧ (asynced ↔ asynced1)), isdir ↔ bv, isdir0 ↔ bv0, asynced1 ↔ asynced0, files1[ino1] = mkfile(m, md0, # links(ino1, dirs), content), buf-opt = none, buf-opt1 = buf-opt0, dirs1 = dirs0, err1 = err0, files = files1, files2 = files0, ino = 0, ino0 = 0, inode = mkinode(ino1, md0, false, # links(ino1, dirs), 0, m), inode1 = inode0, n = m, pageno = m / VFS_PAGE_SIZE, afs-cons(dirs, files1), afs-cons(dirs0, files0), pre-truncate(inode, n, pageno, buf-opt, dirs, files), files1 ~ files0, ino1 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ VFS_PAGE_SIZE = 0, (err0 = ESUCCESS ⊃ files0[ino1].content.stream from m = σ⊥ ∧ (n0 ≤ # buf → ino1 ∈ files0 ∧ files0[ino1].size = m) ∧ files1 -- ino1 = files0 -- ino1 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino1, md0, false, # links(ino1, dirs), 0, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
⟨afs_truncate_internal#(m, m / VFS_PAGE_SIZE; inode, buf-opt, ino0, ino, isdir, err, dirs, files1; asynced)⟩ ( inode = inode0 ∧ buf-opt = buf-opt1 ∧ ino0 = ino2 ∧ ino = ino3 ∧ (isdir ↔ isdir0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced1)), # links(ino1, dirs) = files1[ino1].nlink, files1[ino1] = mkfile(m, md0, files1[ino1].nlink, content), buf-opt = none, ino = 0, ino0 = 0, inode = mkinode(ino1, md0, false, files1[ino1].nlink, 0, m), afs-cons(dirs0, files0), afs-cons(dirs, files1), files1 ~ files0, ino1 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files0[ino1].content.stream from m = σ⊥ ∧ (n0 ≤ # buf → ino1 ∈ files0 ∧ files0[ino1].size = m) ∧ files1 -- ino1 = files0 -- ino1 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino1, md0, false, files1[ino1].nlink, 0, m)

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ¬ none.some?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ pre-truncate(inode, n, pageno, buf-opt, dirs, files) ↔ valid-file-inode(inode, dirs, files) ∧ pageno = inode.size / VFS_PAGE_SIZE ∧ (buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)