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Proof step 766 from proof refine-truncate (previous step)

boolvar1 ↔ boolvar2, boolvar4 ↔ boolvar, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs[ri[inodekey(m)]] = inodenode(key, md0, false, m3, 0, m5), adr4 = adr1, buf-opt = buf-opt0, dirs = abs-dirs(fs, ri), err0 = ENOSPC, files = abs-files(fs, ri), inode = mkinode(m1, md, false, m3, 0, m2), m1 = m, nd = nd2.data:= fill(nd2.data, zero, m2 % VFS_PAGE_SIZE, n0), nd0 = inodenode(inodekey(m), md, false, m3, 0, n), nd1 = truncnode(inodekey(m), m2), nd2 = fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]], p_inode = mkinode(m, md, false, m3, 0, m2), ro = orphans(fs, ri), ro0 = orphans(fs, ri), nd2.data?, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), node-cons(nd.key, nd), node-cons(nd0.key, nd0), node-cons(nd1.key, nd1), orphans-cons(fs, ri, orphans(fs, ri)), orphans-cons(fs, ri, ro0), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), replay-cons-strong(fs, ri, ro0, fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ubifs-cons(fs, ri, ro0, fi, fo, log), datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 % VFS_PAGE_SIZE + n0 ≤ # nd2.data, m2 ≤ n, asynced → boolvar0, ∀ adr1, adr2, adr3. ¬(new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ')) ⊦ ⟨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) ∧ err0 = err1), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, buf-opt0.some?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 767:
boolvar1 ↔ boolvar2, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, fs[ri[inodekey(m)]] = inodenode(key, md0, false, m3, 0, m5), buf-opt = buf-opt0, dirs = abs-dirs(fs, ri), files = abs-files(fs, ri), p_inode = mkinode(m, md, false, m3, 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, m ≠ 0, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data?, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), node-cons ((fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)).key, fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data:= fill(fs[ri[datakey(m, m2 / VFS_PAGE_SIZE)]].data, zero, m2 % VFS_PAGE_SIZE, n0)), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri, ri[datakey(m, m2 / VFS_PAGE_SIZE)] ∈ fs, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, m2 ≤ n, ¬ buf-opt0.some?, asynced → boolvar0, ∀ adr, adr0, adr1. adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1 ⊦ ⟨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) ∧ (asynced → boolvar4) ∧ buf-opt = buf-opt0 ∧ mkinode(m, md, false, m3, 0, m2) = p_inode ∧ (boolvar1 ↔ boolvar2) ∧ ENOSPC = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%⊦ abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)) ↔ orphans(fs0, ri0) = orphans(fs, ri); (s)%⊦ afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)) → orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(orphans(fs, ri)); (s)% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (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)% ⊦ inodekey(m).inode?; (s)% ⊦ node-cons(key0, truncnode(key1, n)) ↔ key0.inode?; (s)% ⊦ truncnode(key, m).key = key; (s)%⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)