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Proof step 124 from proof recovery (previous step)

replay(log0, fs0, fi0, fo0) = ri1 ⊖ orphans(fs0, ri1), fo0.inodes?, orphans(fs0, ri1).inodes?, afs-cons(abs-dirs(fs0, replay-log(log0, fs0, fi0 ⊖ fo0)), abs-files(fs0, replay-log(log0, fs0, fi0 ⊖ fo0))), afs-cons(abs-dirs(fs0, ri1), abs-files(fs0, ri1)), file-node-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0)), file-node-cons(fs0, ri1), log-cons(log0, fs0), orphans-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅), orphans-cons(fs0, ri1, orphans(fs0, ri1)), replay-cons-strong(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅, fi0, fo0, log0), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(replay-log(log0, fs0, fi0 ⊖ fo0)), ri-inj(fi0), ri-inj(ri1), ubifs-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅, fi0, fo0, log0), ubifs-cons(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0) ⊦ # abs-keys(orphans(fs0, replay-log(log0, fs0, fi0 ⊖ fo0))) = 0, abs-keys(orphans(fs0, replay-log(log0, fs0, fi0 ⊖ fo0))) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 125:
replay-log(log0, fs0, fi0 ⊖ fo0) = ri1 ⊖ orphans(fs0, ri1), orphans(fs0, ri1).inodes?, fo0.inodes?, afs-cons(abs-dirs(fs0, ri1), abs-files(fs0, ri1)), afs-cons(abs-dirs(fs0, replay-log(log0, fs0, fi0 ⊖ fo0)), abs-files(fs0, replay-log(log0, fs0, fi0 ⊖ fo0))), file-node-cons(fs0, ri1), file-node-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0)), log-cons(log0, fs0), orphans-cons(fs0, ri1, orphans(fs0, ri1)), orphans-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅), replay-cons-strong(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅, fi0, fo0, log0), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(ri1), ri-inj(fi0), ri-inj(replay-log(log0, fs0, fi0 ⊖ fo0)), ubifs-cons(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0), ubifs-cons(fs0, replay-log(log0, fs0, fi0 ⊖ fo0), ∅, fi0, fo0, log0) ⊦ # abs-keys(orphans(fs0, replay-log(log0, fs0, fi0 ⊖ fo0))) = 0, abs-keys(orphans(fs0, replay-log(log0, fs0, fi0 ⊖ fo0))) = ∅

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[dir-heap-refset]%size-zero: ⊦ # ns ≠ 0 → ns ≠ ∅; (forward) from specification set-basic[dir-heap-refset]% ⊦ replay(log, fs, fi, fo) = replay-log(log, fs, fi ⊖ fo); (s)