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Proof step 27 from proof writepage-prepost (previous step)

F0 = F, buf2 = copy(buf1, m, buf0, n0, n1), dirs0 = dirs, err0 = ESUCCESS, files = files, files0 = files, files1 = files, inode0 = mkinode(m0, md0, boolvar, m2, m3, m4), m5 = m1, md1 = md, n4 = n2, n5 = n3, σ0 = σ, ⌜buf0⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), ((mkinode(m0, md0, boolvar, m2, m3, m4).ino =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ [afs_writepage#(mkinode(m0, md0, boolvar, m2, m3, m4), n3, copy(buf1, m, buf0, n0, n1), dirs; err0, files; asynced)] ( err0 = ESUCCESS ∧ ((inode0.ino =>mkfile(n4, md1, m5, (σ0 to n5 * VFS_PAGE_SIZE) + ⌜buf2⌝ + (σ0 from (n5 + 1) * VFS_PAGE_SIZE)) * F0))(files) ∨ ⌊err0⌋ ∧ files1 = files → err0 = ESUCCESS ∧ ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)) * F) )(files) ∨ ⌊err0⌋ ∧ files0 = files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
err0 = ESUCCESS, ⌜buf0⌝ = (σ from n3 * VFS_PAGE_SIZE) to VFS_PAGE_SIZE, ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, n0 + n1 ≤ # buf0, m + n1 ≤ # buf1, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ [afs_writepage#(mkinode(m0, md0, boolvar, m2, m3, m4), n3, copy(buf1, m, buf0, n0, n1), dirs; err0, files; asynced)] ( err0 = ESUCCESS ∧ ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE) + ⌜copy(buf1, m, buf0, n0, n1)⌝ + (σ from VFS_PAGE_SIZE * n3 + VFS_PAGE_SIZE)) * F) )(files) → ((m0 =>mkfile(n2, md, m1, (σ to n3 * VFS_PAGE_SIZE + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)) * F))(files))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%append-assoc: ⊦ (σ0 + σ3) + σ4 = σ0 + σ3 + σ4; from specification stream[buffer-inf]%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)