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Proof step 65 from proof refine-truncate (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, boolvar3 ↔ true, boolvar ↔ boolvar4, 0 = fs0[ri0[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, buf-opt = some (( datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf) .data:= fill(datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) ).data), buf-opt2 = buf-opt0, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], key = inodekey(m), ks = datakeys(key, n, ri), log = ((log0 + adr1 ') + adr2 ') + adr3 ', n = m2, ri = ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2], ro = orphans(fs0, ri0), ( datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf) .data:= fill(datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) ).data?, datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data?, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).inode?, fs0[ri0[inodekey(m)]].inode?, orphans(fs0, ri0).inodes?, fo.inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks, orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj(ri \ ks), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m2 % VFS_PAGE_SIZE + n0 ≤ # buf-opt0.buf, m2 ≤ n1, m2 % VFS_PAGE_SIZE + (VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) ≤ # datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, VFS_PAGE_SIZE ≥ m2 % VFS_PAGE_SIZE, asynced → boolvar0, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).trunc? ∨ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).inode? ⊦ ⟨p_inode := mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2); buf-opt1 := buf-opt0; files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_truncate#(n1, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, dirs, files, asynced)⟩ ( dirs = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks) ∧ files = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks) ∧ orphans (abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks)) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ mkinode (mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2).ino, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).meta, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).directory, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).nlink, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).nsubdirs, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).size) = p_inode ∧ (boolvar3 ↔ boolvar2) ∧ ESUCCESS = err0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, fs0[ri0[inodekey(m)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 66:
# buf-opt0.buf = VFS_PAGE_SIZE, boolvar ↔ boolvar4, boolvar3 ↔ true, 0 = fs0[ri0[inodekey(m)]].nsubdirs, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, buf-opt = some (( datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf) .data:= fill(datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) ).data), buf-opt2 = buf-opt0, fs = fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], key = inodekey(m), ks = datakeys(key, n, ri), log = ((log0 + adr1 ') + adr2 ') + adr3 ', n = m2, p_inode = mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2), ri = ri0[datakey(m, m2 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2], ro = orphans(fs0, ri0), datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data?, ( datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf) .data:= fill(datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) ).data?, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).inode?, fs0[ri0[inodekey(m)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, buf-opt0.some?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks), log-cons(log0, fs0), log-cons (log0, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-inj(fi), ri-inj(ri0), ri-inj(ri \ ks), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m2 % VFS_PAGE_SIZE + (VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) ≤ # datanode(datakey(m, m2 / VFS_PAGE_SIZE), buf-opt0.buf).data, m2 ≤ n1, m2 % VFS_PAGE_SIZE + n0 ≤ # buf-opt0.buf, VFS_PAGE_SIZE ≥ m2 % VFS_PAGE_SIZE, asynced → boolvar0, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).trunc? ∨ inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).inode? ⊦ ⟨buf-opt1 := buf-opt0; files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_truncate#(n1, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err0, dirs, files, asynced)⟩ ( dirs = abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks) ∧ files = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks) ∧ orphans (abs-dirs (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks), abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1)] [adr3, datanode(datakey(m, m2 / VFS_PAGE_SIZE), fill(buf-opt1.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ], ri \ ks)) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ mkinode (mkinode(m, md, false, fs0[ri0[inodekey(m)]].nlink, 0, m2).ino, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).meta, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).directory, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).nlink, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).nsubdirs, inodenode(inodekey(m), md, false, fs0[ri0[inodekey(m)]].nlink, 0, n1).size) = p_inode ∧ (boolvar3 ↔ boolvar2) ∧ ESUCCESS = err0), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, fs0[ri0[inodekey(m)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ datanode(key, buf).data = buf; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ datanode(key, buf).data:= buf0 = datanode(key, buf0); (s)% ⊦ datanode(key, buf).data?; (s)% ⊦ ¬ inodenode(key, md, boolvar, m, m0, m1).trunc?; (s)%⊦ inodekey(ino) ∈ ri ∧ ri[inodekey(ino)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].inode?; (ss)% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss)