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Proof step 382 from proof inv-truncate (previous step)

m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, 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, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, buf-opt.some?, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, replay-safe(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo)) ∧ ¬ adr3 ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo))) ⊖ inodekey(m0) ) ∧ ( inodekey(m0) ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo))) ⊖ inodekey(m0) ) ⊃ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo))) ⊖ inodekey(m0) ) [datakey(m0, m4 / VFS_PAGE_SIZE), adr3 ] ;(m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo) \ datakeys(inodekey(m0), m4, replay-log(log0, fs0[adr1, truncnode(inodekey(m0), m4)], fi ⊖ fo))) ⊖ inodekey(m0) ) ) = ( ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2])) ⊖ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 383:
m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, 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, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, buf-opt.some?, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, ¬ adr2 ∈ (ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro) ∧ ¬ adr3 ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro))[inodekey(m0), adr2] ;((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro)) ⊖ inodekey(m0) ) ∧ ( inodekey(m0) ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro))[inodekey(m0), adr2] ;((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro)) ⊖ inodekey(m0) ) ⊃ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro))[inodekey(m0), adr2] ;((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro)) ⊖ inodekey(m0) ) [datakey(m0, m4 / VFS_PAGE_SIZE), adr3 ] ;(m ≠ 0 ∨ m0 = ROOT_INO ⊃ ((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro))[inodekey(m0), adr2] ;((ri0 ⊖ ro) \ datakeys(inodekey(m0), m4, ri0 ⊖ ro)) ⊖ inodekey(m0) ) ) = ( ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2])) ⊖ ro

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ adr ∈ ri ⊖ ks; (s)%⊦ ¬ adr ∈ log → replay-log(log, fs[adr, nd], ri) = replay-log(log, fs, ri); (s)%⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) → replay-safe(log, fs, fi ⊖ fo); (ss)%⊦ ¬ adr ∈ log → (replay-safe(log, fs[adr, nd], ri) ↔ replay-safe(log, fs, ri)); (s)