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Proof step 30 from proof eq-io-truncate (previous step)

⟨afs_inode_sync#(new_inode.size:= n; dirs, files)⟩ (dirs = dirs2 ∧ files = files3), boolvar ↔ inode.size ≤ n ∧ pageno0 ≠ 0 ∧ (pageno1 ∈ content ∨ buf-opt.some?), boolvar ↔ boolvar0, asynced ↔ asynced1, ESUCCESS = err0, files1[m] = mkfile(m0, md0, m1, content0), boolvar, content = files2[inode.ino].content, dirs = dirs1, dirs2 = dirs0, files = files2[ino, files2[ino].content:= (content[pageno1, fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)] upto pageno)], files2 = files1, files3 = files0, getinode(inode.ino, dirs2, files3) = p_inode, ino = inode.ino, inode = mkinode(m, md, false, m1, 0, m2), n = n0, new_inode = inode, pageno = min(n, inode.size), pageno = pageno4, pageno0 = inode.size % VFS_PAGE_SIZE, pageno0 = pageno2, pageno1 = m2 / VFS_PAGE_SIZE, pageno3 = 0, pageno5 = 0, some(fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)) = buf-opt0, buf-opt.some?, m ∈ files1, pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ pageno0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode, boolvar1, err, dirs1, files1, boolvar2)⟩ (buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar0) ∧ err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0), VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
⟨afs_inode_sync#(mkinode(m, md, false, m1, 0, n0); dirs1, files)⟩ (dirs1 = dirs0 ∧ files = files0), # buf-opt.buf = VFS_PAGE_SIZE, files1[m] = mkfile(m0, md0, m1, content0), files = files1 [m, mkfile(m0, md0, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md, false, m1, 0, m2), some(fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)) = buf-opt0, m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, m ∈ files1, m2 ≤ n0 ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode, boolvar1, err, dirs1, files1, boolvar2)⟩ ( buf-opt = buf-opt0 ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar1 ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files0)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2).size:= m6 = mkinode(m, md, boolvar, m0, m1, m6); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)