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Proof step 397 from proof inv-truncate (previous step)

VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key, md, false, m, 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-cons-strong(fs0, ri0, ro, fi, fo, log0), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), key0 ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ], adr1 = adr2, adr2 = (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ], m0 = 0, buf-opt.some?, adr1 ∈ log0, adr2 ∈ log0, (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ] ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ] ∈ fs0, (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ] ∈ ri0, inodekey(m0) ∈ ro, m = 0 ∧ m0 ≠ ROOT_INO

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 398:
VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m0)]] = inodenode(key, md, false, m, m1, m2), fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), 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-cons-strong(fs0, ri0, ro, fi, fo, log0), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, key0 ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ), m4 ≤ n1, m ≠ 0 ∨ m0 = ROOT_INO ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = ((ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro)[key0], adr2 = (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ], m0 = 0, buf-opt.some?, inodekey(m0) ∈ ro, (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ] ∈ ri0, (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ] ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, (m ≠ 0 ∨ m0 = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro) ⊖ inodekey(m0) ) [key0 ] ∈ log0, adr2 ∈ log0, adr1 ∈ log0, m = 0 ∧ m0 ≠ ROOT_INO

Rule argument

pos: right 2

Additional information

Used simplifier rules: ⊦ key ∈ ri ⊖ key0 ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0); (ws)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)