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Proof step 25 from proof writepage-prepost (previous step)

err0 = ESUCCESS, files0 = files, ⌜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 ≤ VFS_PAGE_SIZE, m + n1 ≤ # buf1, n0 + n1 ≤ # buf0 ⊦ [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 + n0) + ((⌜buf1⌝ from m) to n1) + (σ from n3 * VFS_PAGE_SIZE + n0 + n1)) * F))(files) ∨ ⌊err0⌋ ∧ files0 = files)

User applied rule insert program lemma

And obtained the following new goals

Proof step 26:
afs-cons(dirs, files), files0 = files, ((inode.ino =>mkfile(n0, md, m, σ) * F))(files) ⊦ [afs_writepage#(inode, n, buf, dirs; err, files; asynced)] ( err = ESUCCESS ∧ ((inode.ino =>mkfile(n0, md, m, (σ to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (σ from (n + 1) * VFS_PAGE_SIZE)) * F))(files) ∨ ⌊err⌋ ∧ files0 = files)
Proof step 27:
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)

Rule argument

spec: afs-contracts name: writepage-prepost seq: afs-cons(dirs, files), files0 = files, ((inode.ino =>mkfile(n0, md, m, σ) * F))(files) ⊦ [afs_writepage#(inode, n, buf, dirs; err, files; asynced)] ( err = ESUCCESS ∧ (( inode.ino =>mkfile (n0, md, m, (σ to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (σ from (n + 1) * VFS_PAGE_SIZE) ) * F) )(files) ∨ ⌊err⌋ ∧ files0 = files) subst: [dirs, buf, n, inode, files, err, asynced, n0, md, m, σ, F, files0] → [dirs, copy(buf1, m, buf0, n0, n1), n3, mkinode(m0, md0, boolvar, m2, m3, m4), files, err0, asynced, n2, md, m1, σ, F, files] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)