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Proof step 868 from proof refine-truncate (previous step)

boolvar4 ↔ boolvar, boolvar1 ↔ boolvar2, fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m1, 0, m4), adr = adr5, adr0 = adr3, adr4 = adr2, buf-opt = buf-opt0, dirs = abs-dirs(fs0, ri), err = ESUCCESS, files = abs-files(fs0, ri), fs = fs0[adr1, nd0][adr2, nd], inode = mkinode(m, md, false, m1, 0, m2), log = (log0 + adr1) + adr2, nd = inodenode(inodekey(m), md, false, m1, 0, n), nd0 = truncnode(inodekey(m), m2), ro = orphans(fs0, ri), ro0 = orphans(fs0, ri), fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + adr2 ', fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri, m2 ≤ n, asynced → boolvar0 ⊦ [aubifs_core_index_store#(inodekey(m), adr4, fi, ro0, fo, fs, log, boolvar4; ri); aubifs_core_index_truncate#(inodekey(m), min(n, m2), fi, ro0, fo, fs, log, boolvar4; ri); boolvar1 := false; inode := mkinode (inode.ino, inodenode(inodekey(m), md, false, m1, 0, n).meta, inodenode(inodekey(m), md, false, m1, 0, n).directory, inodenode(inodekey(m), md, false, m1, 0, n).nlink, inodenode(inodekey(m), md, false, m1, 0, n).nsubdirs, inodenode(inodekey(m), md, false, m1, 0, n).size); if boolvar1 then buf-opt := some(nd.data)] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨p_inode := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err1, dirs, files, asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ err = err1)), m2 % VFS_PAGE_SIZE = 0, buf-opt0.some?, dups(adr1 ' + adr2 '), datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 869:
fs0[ri[inodekey(m)]] = inodenode(key, md0, false, m1, 0, m4), dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), ro = orphans(fs0, ri), m2 % VFS_PAGE_SIZE ≠ 0, adr1 ≠ adr2, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), inodekey(m) ∈ ri, ri[inodekey(m)] ∈ fs0, m2 ≤ n, ¬ buf-opt0.some?, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, asynced → boolvar0 ⊦ [aubifs_core_index_store# (inodekey(m), adr2, fi, orphans(fs0, ri), fo, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], (log0 + adr1 ') + adr2 ', boolvar4 ; ri); aubifs_core_index_truncate# (inodekey(m), min(n, m2), fi, ro, fo, fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], (log0 + adr1 ') + adr2 ', boolvar4 ; ri); boolvar1 := false; inode := mkinode (m, inodenode(inodekey(m), md, false, m1, 0, n).meta, inodenode(inodekey(m), md, false, m1, 0, n).directory, inodenode(inodekey(m), md, false, m1, 0, n).nlink, inodenode(inodekey(m), md, false, m1, 0, n).nsubdirs, inodenode(inodekey(m), md, false, m1, 0, n).size); buf-opt := buf-opt0; if boolvar1 then buf-opt := some(inodenode(inodekey(m), md, false, m1, 0, n).data)] ( ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri, ro, fi, fo, (log0 + adr1 ') + adr2 ') ∧ file-node-cons(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri) ∧ orphans-cons(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri, ro) ∧ ri-inj(ri) ∧ m ≠ 0 → ⟨p_inode := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, p_inode, boolvar2, err1, dirs, files, asynced)⟩ ( dirs = abs-dirs(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri) ∧ files = abs-files(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri) ∧ orphans (abs-dirs(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri), abs-files(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n)], ri)) = abs-keys(ro) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ inode = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ ESUCCESS = err1))

Rule argument

Additional information

Used simplifier rules: log-cons-2: ⊦ log-cons(log, fs) ∧ ¬ adr0 ∈ fs ∧ ¬ adr1 ∈ fs ∧ adr0 ≠ adr1 → log-cons(log, fs[adr0, nd0][adr1, nd1]);% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)% ⊦ inodekey(m).ino = m; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ node-cons(key0, truncnode(key1, n)) ↔ key0.inode?; (s)% ⊦ truncnode(key, m).key = key; (s)% ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]); (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr0, nd] ↔ adr = adr0 ∨ adr ∈ fs; (ws)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)% ⊦ log-cons(adr ', fs) ↔ adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ ax + adr = ax + adr '; (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)