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Proof step 3 from proof write-loop-term (previous step)

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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
¬ boolvar, inode = mkinode(m, md, boolvar, m0, m1, m2), m0 = files[m].nlink, m1 = 0, afs-cons(dirs, files), m ∈ files, n ≤ # buf, n0 + n ≤ n1, n1 ≤ # buf + n0 ⊦ ⟪vfs_write_loop#(n0, inode, n1, buf, dirs; n, err, files, asynced)⟫ (m ∈ files ∧ m0 = files[m].nlink)

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, m2] → [inode, m, md, boolvar, m0, m1, m2]

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, m, md, boolvar, m0, m1, m2