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Proof step 11 from proof ri-closed-gc (previous step)

# kx0 = # ax1, new(ax1, fs[adr, fs[ri[key]]]), new(ax1, fs), ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[adr, fs[ri[key]]][ri[kx0]]], ro), ri-closed(ri, fs, ro), ri-cons(ri, fs), adr ∈ ri[kx0], key ∈ ri, kx0.toSet ⊆ dom ri ⊦ dups(kx0), dups(ax1), ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[ri[kx0]]], ro), adr ∈ fs, key ∈ kx0, adr ∈ ax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# kx0 = # ax1, new(ax1, fs), new(ax1, fs[adr, fs[ri[key]]]), ri-closed(ri, fs, ro), ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[adr, fs[ri[key]]][ri[kx0]]], ro), ri-cons(ri, fs), key ∈ ri, adr ∈ ri[kx0], adr ∈ ri, kx0.toSet ⊆ dom ri ⊦ dups(ax1), dups(kx0), ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[ri[kx0]]], ro), adr ∈ ax1, key ∈ kx0, adr ∈ fs

Rule argument

Additional information

Used simplifier rules: in-read-in-dom: ⊦ kx.toSet ⊆ dom ri ∧ adr ∈ ri[kx] → adr ∈ ri; (forward) from specification aubifs-base