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

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

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 17:
# kx = # ax, fs = fs0[ax, fs0[ri0[kx]]], log = log0 + ax, ri = ri0[kx, ax], ax.toSet ∩ log0.toSet = ∅, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), new(ax, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), kx.toSet ⊆ dom ri0 ⊦ [choose as with as ∩ range ri = ∅ ∧ log.toSet ∩ as = ∅ in fs := fs \ as; boolvar := ?] ( ri-inj(ri0[kx, ax]) ∧ log-cons(log0, fs) ∧ log-cons(ax, fs) ∧ ri-cons(ri0[kx, ax], fs) → ubifs-cons(fs, ri0[kx, ax], ro, fi, fo, log0 + ax) ∧ replay-cons-strong(fs, ri0[kx, ax], ro, fi, fo, log0 + ax) ∧ file-node-cons(fs, ri0[kx, ax]) ∧ orphans-cons(fs, ri0[kx, ax], ro)), dups(kx), dups(ax)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_gc_drop#(RI, LOG; FS) {choose AS with AS ∩ range RI = ∅ ∧ LOG.toSet ∩ AS = ∅ in FS := FS \ AS };