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Proof step 34 from proof inv-evict (previous step)

replay(log, fs, fi, fo) = ri1 ⊖ ro0, 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, ∀ ino. inodekey(ino) ∈ ro0 → links(ino, fs, ri1) = ∅, ∀ ino. inodekey(ino) ∈ ro0 → dentrykeys(inodekey(ino), ri1) = ∅ ⊦ # ro0 = 0, m = ROOT_INO, replay-log(log, fs, fi ⊖ fo) = ((ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ⊖ (ro0 -- inodekey(m)), ro0 = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
replay-log(log, fs, fi ⊖ fo) = ri1 ⊖ ro0, 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, m = ROOT_INO, ro0 = ∅, ri1 ⊖ ro0 = ((ri1 \ datakeys(inodekey(m), ri1)) -- inodekey(m)) ⊖ (ro0 -- inodekey(m))

Rule argument

Additional information

Used simplifier rules: ⊦ replay(log, fs, fi, fo) = replay-log(log, fs, fi ⊖ fo); (s)