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Proof step 105 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), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.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(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 ≤ n1 ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, inodekey(m) ∈ ro, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, ∀ key. ( key ∈ ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ) ↔ key ∈ ( ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m3, ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ⊖ ro) ∧ ( key ∈ ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ) → ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ) [key ] = ( ( ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m3, ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ⊖ ro )[key ]), m0 = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 106:
# 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, 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 ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, inodekey(m) ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO, ( key0 ∈ ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ) ↔ key0 ∈ ( ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m3, ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ⊖ ro) ∧ ( key0 ∈ ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ) → ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro ;((ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro) ⊖ inodekey(m) ) ) [key0 ] = ( ( ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m3, ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ⊖ ro )[key0 ])

Proof step 105 from proof inv-truncate (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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