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Proof step 27 from proof replay-safe-gc-copy (previous step)

# ax0 = # kx1, ro.inodes?, new(ax0, fs), orphans-cons(fs, ri, ro), ri-closed(ri, fs, ro), ri-cons(ri, fs), key ∈ ri, kx1.toSet ⊆ dom ri, # kx1 = # kx1 ∧ ro.inodes? ∧ new(ax0, fs[adr, fs[ri[key]]]) ∧ orphans-cons(fs[adr, fs[ri[key]]], ri[key, adr], ro) ∧ ri-closed(ri[key, adr], fs[adr, fs[ri[key]]], ro) ∧ ri-cons(ri[key, adr], fs[adr, fs[ri[key]]]) ∧ kx1.toSet ⊆ dom ri[key, adr] → dups(kx1) ∨ replay-safe(ax0, fs[adr, fs[ri[key]]][ax0, fs[adr, fs[ri[key]]][ri[key, adr][kx1]]], ri[key, adr] ⊖ ro) ⊦ dups(ax0), dups(kx1), replay-safe(ax0, fs[ax0, fs[ri[kx1]]], ri[key, adr] ⊖ ro), adr ∈ ax0, adr ∈ fs, key ∈ kx1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: orphans-cons-gc-one: ⊦ key ∈ ri ∧ ¬ adr ∈ fs ∧ orphans-cons(fs, ri, ro) ∧ ri-cons(ri, fs) → orphans-cons(fs[adr, fs[ri[key]]], ri[key, adr], ro);% ⊦ new(ax, fs) → (new(ax, fs[adr, nd]) ↔ ¬ adr ∈ ax); (ss)% ⊦ ¬ key ∈ kx → ri[key, adr][kx] = ri[kx]; (s)% ⊦ key ∈ ri → dom ri ++ key = dom ri; (s)% ⊦ dom ri[key, adr] = dom ri ++ key; (s)%⊦ key ∈ ri ∧ ¬ adr ∈ fs ∧ ri-cons(ri, fs) → ri-cons(ri[key, adr], fs[adr, fs[ri[key]]]); (s)%⊦ key ∈ ri ∧ ¬ adr ∈ fs ∧ ri-closed(ri, fs, ro) ∧ ri-cons(ri, fs) → ri-closed(ri[key, adr], fs[adr, fs[ri[key]]], ro); (s)