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Proof step 2 from proof writepage-prepost (previous step)

files0 = files, ((inode.ino =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), inode.ino ∈ files, n0 + n1 ≤ VFS_PAGE_SIZE, m + n1 ≤ # buf ⊦ [vfs_writepage#(inode, n, buf, m, n0, n1, dirs; err, files, asynced)] ( err = ESUCCESS ∧ ((inode.ino =>mkfile(n2, md, m1, (σ to n * VFS_PAGE_SIZE + n0) + ((⌜buf⌝ from m) to n1) + (σ from n * VFS_PAGE_SIZE + n0 + n1)) * F) )(files) ∨ ⌊err⌋ ∧ files0 = files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
files0 = files, inode = mkinode(m0, md0, boolvar, m2, m3, m4), ((m0 =>mkfile(n2, md, m1, σ) * F))(files), afs-cons(dirs, files), m0 ∈ files, m + n1 ≤ # buf, n0 + n1 ≤ VFS_PAGE_SIZE ⊦ [vfs_writepage#(inode, n, buf, m, n0, n1, dirs; err, files, asynced)] ( err = ESUCCESS ∧ ((m0 =>mkfile(n2, md, m1, (σ to n * VFS_PAGE_SIZE + n0) + ((⌜buf⌝ from m) to n1) + (σ from n * VFS_PAGE_SIZE + n0 + n1)) * F))(files) ∨ ⌊err⌋ ∧ files0 = files)

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1] → [inode, m0, md0, boolvar, m2, m3]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode, m0, md0, boolvar, m2, m3