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Proof step 9 from proof inv-gc (previous step)

# kx = # ax, fs = fs0[ax, fs0[ri[kx]]], log = log0 + ax, ax.toSet ∩ log0.toSet = ∅, ro.inodes?, fo.inodes?, log-cons(log0, fs0), new(ax, fs0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), kx.toSet ⊆ dom ri ⊦ ⟪aubifs_core_gc_drop#(ri[kx, ax], log; fs); boolvar := ?⟫ (log-cons(log, fs) ∧ ri-cons(ri[kx, ax], fs)), dups(ax), dups(kx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# kx = # ax, fs = fs0[ax, fs0[ri[kx]]], ax.toSet ∩ log0.toSet = ∅, fo.inodes?, ro.inodes?, log-cons(log0, fs0), new(ax, fs0), ri-cons(ri, fs0), ri-inj(fi), ri-inj(ri), kx.toSet ⊆ dom ri, ¬ dups(kx), ¬ dups(ax) ⊦ ⟪aubifs_core_gc_drop#(ri[kx, ax], log0 + ax; fs); boolvar := ?⟫ (log-cons(log0, fs) ∧ log-cons(ax, fs) ∧ ri-cons(ri[kx, ax], fs))

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)