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Proof step 782 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE, ∃ key. key ∈ (ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro ∧ ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[key] = adr2 ⊦ adr1 = adr2, m = 0, inodekey(m) ∈ ro, adr2 ∈ fs0, adr1 ∈ fs0, adr2 ∈ log0, adr1 ∈ log0, m3 ≤ n0 ∧ m3 % VFS_PAGE_SIZE ≠ 0, m0 = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 783:
fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, key0 ∈ ri0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE, key0.data? → ¬ inodekey(key0.ino) ∈ ro, ¬ key0.data? ∨ key0.ino ≠ m ∨ ¬ min(n0, m3) ≤ key0.part * VFS_PAGE_SIZE ⊦ adr1 = ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[key0], m = 0, adr1 ∈ log0, ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[key0] ∈ log0, adr1 ∈ fs0, ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[key0] ∈ fs0, inodekey(m) ∈ ro, key0 ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO, m3 ≤ n0 ∧ m3 % VFS_PAGE_SIZE ≠ 0

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws)