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Proof step 16 from proof refine-gc (previous step)

# kx = # ax, dirs = abs-dirs(fs0, ri), files = abs-files(fs0, ri), fs = fs0[ax, fs0[ri[kx]]], log = log0 + ax, ro = orphans(fs0, ri), ax.toSet ∩ log0.toSet = ∅, fo.inodes?, orphans(fs0, ri).inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), kx.toSet ⊆ dom ri, asynced → boolvar ⊦ [aubifs_core_gc_drop#(ri[kx, ax], log; fs); boolvar := ?] ( ubifs-cons(fs, ri[kx, ax], ro, fi, fo, log) ∧ replay-cons-strong(fs, ri[kx, ax], ro, fi, fo, log) ∧ file-node-cons(fs, ri[kx, ax]) ∧ orphans-cons(fs, ri[kx, ax], ro) ∧ ri-inj(ri[kx, ax]) ∧ log-cons(log, fs) → ⟨asynced := ?⟩ ( dirs = abs-dirs(fs, ri[kx, ax]) ∧ files = abs-files(fs, ri[kx, ax]) ∧ orphans(abs-dirs(fs, ri[kx, ax]), abs-files(fs, ri[kx, ax])) = abs-keys(ro) ∧ (asynced → boolvar))), dups(ax), dups(kx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# kx = # ax, fs = fs0[ax, fs0[ri[kx]]], ax.toSet ∩ log0.toSet = ∅, orphans(fs0, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri), abs-files(fs0, ri)), file-node-cons(fs0, ri), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0, ri, orphans(fs0, ri)), replay-cons-strong(fs0, ri, orphans(fs0, ri), fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, orphans(fs0, ri), fi, fo, log0), kx.toSet ⊆ dom ri, ¬ dups(kx), ¬ dups(ax), asynced → boolvar ⊦ [aubifs_core_gc_drop#(ri[kx, ax], log0 + ax; fs); boolvar := ?] ( ubifs-cons(fs, ri[kx, ax], orphans(fs0, ri), fi, fo, log0 + ax) ∧ replay-cons-strong(fs, ri[kx, ax], orphans(fs0, ri), fi, fo, log0 + ax) ∧ file-node-cons(fs, ri[kx, ax]) ∧ orphans-cons(fs, ri[kx, ax], orphans(fs0, ri)) ∧ ri-inj(ri[kx, ax]) ∧ log-cons(log0, fs) ∧ log-cons(ax, fs) → ⟨asynced := ?⟩ ( abs-dirs(fs0, ri) = abs-dirs(fs, ri[kx, ax]) ∧ abs-files(fs0, ri) = abs-files(fs, ri[kx, ax]) ∧ orphans(abs-dirs(fs, ri[kx, ax]), abs-files(fs, ri[kx, ax])) = abs-keys(orphans(fs0, ri)) ∧ (asynced → boolvar)))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ log-cons(log0 + log1, fs) ↔ log-cons(log0, fs) ∧ log-cons(log1, fs); (s)