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Proof step 22 from proof refine-gc (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# 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))

Rule argument

Additional information

Used simplifier rules: ⊦ range ri ∩ as = ∅ → abs-files(fs \ as, ri) = abs-files(fs, ri); (s)% ⊦ range ri ∩ as = ∅ → abs-dirs(fs \ as, ri) = abs-dirs(fs, ri); (s)%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%unc: ⊦ as ∪ as0 = as0 ∪ as; from specification set-union[node-store]%una: ⊦ (as ∪ as0) ∪ as1 = as ∪ as0 ∪ as1; from specification set-union[node-store]% ⊦ as ∩ (as0 ∪ as1) = ∅ ↔ as ∩ as0 = ∅ ∧ as ∩ as1 = ∅; (ws)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ (ax + ax0).toSet = ax.toSet ∪ ax0.toSet; (s)