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Proof step 50 from proof inv-evict (previous step)

replay-log(log, fs, fi ⊖ fo) = (ri1 \ ro0) \ datakeys(ro0, ri1), ro0.inodes?, fo.inodes?, file-node-cons(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)), file-node-cons(fs, ri1), log-cons(log, fs), orphans-cons(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), ro0 -- inodekey(m)), orphans-cons(fs, ri1, ro0), replay-safe(log, fs, fi ⊖ fo), ri-inj(ri1), ri-inj(fi), ubifs-cons(fs, ri1, ro0, fi, fo, log), inodekey(m) ∈ ro0, inodekey(m) ∈ ri1, ∀ ino. inodekey(ino) ∈ ro0 → dentrykeys(inodekey(ino), ri1) = ∅, ∀ ino. inodekey(ino) ∈ ro0 → links(ino, fs, ri1) = ∅ ⊦ # ro0 = 0, (key ∈ ri1 ∧ key.data? ∧ inodekey(key.ino) ∈ ro0 ⊃ (∅)[key];(key ∈ ro0 ⊃ (∅)[key];ri1[key])) = (inodekey(m) = key ⊃ (∅)[inodekey(m)] ;( key ∈ datakeys(ro0, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) \ datakeys(inodekey(m), (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ⊃ (∅)[key] ;(key ∈ ro0 ⊃ (∅)[key];(key ∈ ri1 ∧ key.data? ∧ key.ino = m ⊃ (∅)[key];ri1[key])) ) ), m = ROOT_INO, ro0 = ∅, key ∈ ri1 ∧ ¬ key ∈ ro0 ∧ ¬ key.data?

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 51:
replay-log(log, fs, fi ⊖ fo) = (ri1 \ ro0) \ datakeys(ro0, ri1), fo.inodes?, ro0.inodes?, file-node-cons(fs, ri1), file-node-cons(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)), log-cons(log, fs), orphans-cons(fs, ri1, ro0), orphans-cons(fs, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m), ro0 -- inodekey(m)), replay-safe(log, fs, fi ⊖ fo), ri-inj(fi), ri-inj(ri1), ubifs-cons(fs, ri1, ro0, fi, fo, log), inodekey(m) ∈ ri1, inodekey(m) ∈ ro0, key ∈ ri1, ∀ ino. inodekey(ino) ∈ ro0 → links(ino, fs, ri1) = ∅, ∀ ino. inodekey(ino) ∈ ro0 → dentrykeys(inodekey(ino), ri1) = ∅ ⊦ # ro0 = 0, (key ∈ ri1 ∧ key.data? ∧ inodekey(key.ino) ∈ ro0 ⊃ (∅)[key];(key ∈ ro0 ⊃ (∅)[key];ri1[key])) = (inodekey(m) = key ⊃ (∅)[inodekey(m)] ;( key ∈ datakeys(ro0, (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) \ datakeys(inodekey(m), (ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ⊃ (∅)[key] ;(key ∈ ro0 ⊃ (∅)[key];(key ∈ ri1 ∧ key.data? ∧ key.ino = m ⊃ (∅)[key];ri1[key])) ) ), m = ROOT_INO, ro0 = ∅, key ∈ ri1 ∧ ¬ key ∈ ro0 ∧ ¬ key.data?

Rule argument

fma: key ∈ ri1

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s) Used formulas: key ∈ ri1