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Proof step 139 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), datakey(ino, n) = datakey(m, m3 / VFS_PAGE_SIZE), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, ro.inodes?, fo.inodes?, buf-opt.some?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), replay-safe(log0, fs0, fi ⊖ fo), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m3 ≤ n1, datakey(m, n) ≠ datakey(m, m3 / VFS_PAGE_SIZE) ∧ ¬ datakey(m, n) ∈ ri0 ∨ ino ≠ m ∨ ¬ m3 ≤ n * VFS_PAGE_SIZE, m0 ≠ 0 ∨ m = ROOT_INO, datakey(ino, n) = datakey(m, m3 / VFS_PAGE_SIZE) ∨ datakey(ino, n) ∈ ri0 ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, inodekey(ino) ∈ ro, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, inodekey(m) ∈ ro, inodekey(m) ∈ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro, datakey(ino, n) ∈ ri0 ∧ (ino ≠ m ∨ ¬ m3 ≤ n * VFS_PAGE_SIZE), m0 = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 140:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.inodes?, buf-opt.some?, m3 / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n1, m3 / VFS_PAGE_SIZE * VFS_PAGE_SIZE < m3, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), replay-safe(log0, fs0, fi ⊖ fo), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 ≤ n1, m0 ≠ 0 ∨ m = ROOT_INO ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, inodekey(m) ∈ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, inodekey(m) ∈ ro, datakey(m, m3 / VFS_PAGE_SIZE) ∈ ri0, m0 = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)