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Proof step 23 from proof refine-gc (previous step)

# kx = # ax, ax.toSet ∩ log0.toSet = ∅, as ∩ range ri0[kx, ax] = ∅, as ∩ log0.toSet = ∅, as ∩ ax.toSet = ∅, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax]), file-node-cons(fs0, ri0), log-cons(log0, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(ax, fs0[ax, fs0[ri0[kx]]] \ as), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax], orphans(fs0, ri0), fi, fo, log0 + ax), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj(ri0[kx, ax]), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0[ax, fs0[ri0[kx]]] \ as, ri0[kx, ax], orphans(fs0, ri0), fi, fo, log0 + ax), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), kx.toSet ⊆ dom ri0, asynced0 → boolvar0 ⊦ dups(ax), dups(kx), abs-dirs(fs0, ri0) = abs-dirs(fs0[ax, fs0[ri0[kx]]], ri0[kx, ax]) ∧ abs-files(fs0, ri0) = abs-files(fs0[ax, fs0[ri0[kx]]], ri0[kx, ax]) ∧ orphans(abs-dirs(fs0[ax, fs0[ri0[kx]]], ri0[kx, ax]), abs-files(fs0[ax, fs0[ri0[kx]]], ri0[kx, ax])) = abs-keys(orphans(fs0, ri0))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 3

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