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Proof step 632 from proof inv-truncate (previous step)

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-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), key0 ∈ ri0, inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, m4 ≤ n0, key0.data? → ¬ inodekey(key0.ino) ∈ ro, ¬ key0.data? ∨ key0.ino ≠ m0 ∨ ¬ m4 ≤ key0.part * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = ((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro)[key0], m0 = 0, buf-opt.some?, key0 ∈ ro, inodekey(m0) ∈ ro, ((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro)[key0] ∈ fs0, adr1 ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro)[key0] ∈ log0, adr1 ∈ log0, m = 0 ∧ m0 ≠ ROOT_INO, key0 ∈ ri0 \ datakeys(inodekey(m0), m4, ri0) ∧ ¬ key0 ∈ ro ∧ ¬ key0.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 633:
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-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), datakey(ino, n) ∈ ri0, inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(ino) ∈ ri0, m4 ≤ n0, ino ≠ m0 ∨ ¬ m4 ≤ n * VFS_PAGE_SIZE ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = ((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro)[datakey(ino, n)], m0 = 0, fs0[ri0[inodekey(ino)]].directory, buf-opt.some?, inodekey(m0) ∈ ro, ((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro)[datakey(ino, n)] ∈ fs0, adr1 ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ((ri0 \ datakeys(inodekey(m0), m4, ri0)) ⊖ ro)[datakey(ino, n)] ∈ log0, adr1 ∈ log0, inodekey(ino) ∈ ro, m = 0 ∧ m0 ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (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)