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Proof step 2 from proof write-loop-term (previous step)

afs-cons(dirs, files), valid-file-inode(inode, dirs, files), n1 - n0 ≤ # buf, n0 + n ≤ n1 ⊦ ⟪vfs_write_loop#(n0, inode, n1, buf, dirs; n, err, files, asynced)⟫ valid-file-inode(inode, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
inode.nlink = files[inode.ino].nlink, inode.nsubdirs = 0, afs-cons(dirs, files), inode.ino ∈ files, n1 ≤ # buf + n0, n0 + n ≤ n1, n ≤ # buf, ¬ inode.directory ⊦ ⟪vfs_write_loop#(n0, inode, n1, buf, dirs; n, err, files, asynced)⟫ (inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (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)% ⊦ m ≤ n ↔ ¬ n < m; (ss)