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Proof step 8 from proof eq-io-truncate (previous step)

⟨afs_truncate_internal#(n0, inode.size / VFS_PAGE_SIZE; inode, buf-opt, pageno0, pageno, boolvar, err, dirs1, files1; asynced)⟩ ( inode = p_inode ∧ buf-opt = buf-opt0 ∧ pageno0 = pageno2 ∧ pageno = pageno4 ∧ (boolvar ↔ boolvar0) ∧ err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced1)), inode.nlink = files1[inode.ino].nlink, inode.nsubdirs = 0, pageno = 0, pageno0 = 0, inode.ino ∈ files1, ¬ inode.directory, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨afs_truncate#(n0, inode.size / VFS_PAGE_SIZE; buf-opt, inode, boolvar, err, dirs1, files1, boolvar2)⟩ (buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar ↔ boolvar0) ∧ err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
⟨afs_truncate_internal#(n0, m2 / VFS_PAGE_SIZE; inode, buf-opt, pageno0, pageno, boolvar, err, dirs1, files1; asynced)⟩ ( inode = p_inode ∧ buf-opt = buf-opt0 ∧ pageno0 = pageno2 ∧ pageno = pageno4 ∧ (boolvar ↔ boolvar0) ∧ err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced1)), ¬ boolvar1, inode = mkinode(m, md, boolvar1, m0, m1, m2), m0 = files1[m].nlink, m1 = 0, pageno = 0, pageno0 = 0, m ∈ files1, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode, boolvar, err, dirs1, files1, boolvar2)⟩ (buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar ↔ boolvar0) ∧ err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0)

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, boolvar1, 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, boolvar1, m0, m1, m2