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Proof step 331 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, boolvar ↔ mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).size ≤ n ∧ pageno0 ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?), 0 = fs[ri[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, buf-opt = buf-opt0, content = abs-files(fs, ri)[mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).ino].content, dirs = abs-dirs(fs, ri), files = files0[ino, files0[ino].content:= (content[pageno1, fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)] upto pageno)], files0 = abs-files(fs, ri), ino = mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).ino, new_inode = mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2), pageno = min(n, mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).size), pageno0 = mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).size % VFS_PAGE_SIZE, pageno1 = m2 / VFS_PAGE_SIZE, fs[ri[inodekey(m)]].inode?, fo.inodes?, orphans(fs, ri).inodes?, buf-opt0.some?, buf-opt.some?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, pageno0 + (VFS_PAGE_SIZE - pageno0) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ pageno0, asynced → boolvar0, mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).size ≤ n → pageno0 ≠ 0 → VFS_PAGE_SIZE ≠ 0, ∀ adr1, adr2, adr3. adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr3 ∈ fs ∨ adr1 = adr2 ∨ adr1 = adr3 ∨ adr2 = adr3 ⊦ ⟨afs_inode_sync#(new_inode.size:= n; dirs, files); inode := getinode(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar4) ∧ buf-opt0 = some(fill(buf-opt.buf, zero, pageno0, VFS_PAGE_SIZE - pageno0)) ∧ mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2) = inode ∧ (boolvar2 ↔ boolvar) ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar4) ∧ ENOSPC = err), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, fs[ri[inodekey(m)]].directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 332:
# buf-opt0.buf = VFS_PAGE_SIZE, 0 = fs[ri[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri) [m, mkfile (fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].meta, fs[ri[inodekey(m)]].nlink, abs-content(m, fs, ri)[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], m2 % VFS_PAGE_SIZE ≠ 0, fs[ri[inodekey(m)]].inode?, fo.inodes?, orphans(fs, ri).inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, ¬ fs[ri[inodekey(m)]].directory, asynced → boolvar0, ∀ adr1, adr2, adr3. adr1 ∈ fs ∨ adr2 ∈ fs ∨ adr3 ∈ fs ∨ adr1 = adr2 ∨ adr1 = adr3 ∨ adr2 = adr3 ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, n); dirs, files); inode := getinode(mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2).ino, dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ (asynced → boolvar4) ∧ buf-opt0 = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)) ∧ mkinode(m, md, false, fs[ri[inodekey(m)]].nlink, 0, m2) = inode ∧ boolvar2 ∧ ENOSPC = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced → boolvar4) ∧ ENOSPC = err)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)% ⊦ n ∈ abs-content(ino, fs, ri) ↔ datakey(ino, n) ∈ ri; (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)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (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).size = m2; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)