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Proof step 419 from proof inv-truncate (previous step)

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, inodekey(m0) ∈ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro, m4 ≤ n1, key0 = datakey(m0, m4 / VFS_PAGE_SIZE) ∨ 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) ), m ≠ 0 ∨ m0 = ROOT_INO ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, buf-opt.some?, inodekey(m0) ∈ ro, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, key0 ∈ ri0 ∧ (¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE) ∧ ¬ key0 ∈ ro ∧ (key0.data? → ¬ inodekey(key0.ino) ∈ ro), m = 0 ∧ m0 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 420:
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), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, m4 ≤ n1, m ≠ 0 ∨ m0 = ROOT_INO, key0 = datakey(m0, m4 / VFS_PAGE_SIZE) ∨ key0 ∈ (ri0 \ datakeys(inodekey(m0), m4, ri0))[inodekey(m0), adr2] ⊖ ro ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, buf-opt.some?, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ ri0, inodekey(m0) ∈ ro, m = 0 ∧ m0 ≠ ROOT_INO, key0 ∈ ri0 ∧ (¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE) ∧ ¬ key0 ∈ ro ∧ (key0.data? → ¬ inodekey(key0.ino) ∈ ro)

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ ¬ inodekey(m).data?; (s)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws)