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Proof step 23 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, ∀ kx0, ro0, fs0, ri0. # kx1 = # kx0 ∧ ro0.inodes? ∧ new(ax0, fs0) ∧ orphans-cons(fs0, ri0, ro0) ∧ ri-closed(ri0, fs0, ro0) ∧ ri-cons(ri0, fs0) ∧ kx0.toSet ⊆ dom ri0 → dups(kx0) ∨ replay-safe(ax0, fs0[ax0, fs0[ri0[kx0]]], ri0 ⊖ ro0) ⊦ dups(kx1), dups(ax0), replay-safe(ax0, fs[ax0, fs[ri[kx1]]], replay-one(adr, fs[ri[key]], ri ⊖ ro)), key ∈ kx1, adr ∈ fs, adr ∈ ax0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: replay-one-update seq: ⊦ ri-closed(ri, fs, ro) ∧ ri-cons(ri, fs) ∧ key ∈ ri ∧ ro.inodes? ∧ orphans-cons(fs, ri, ro) → replay-one(adr, fs[ri[key]], ri ⊖ ro) = ri[key, adr] ⊖ ro subst: [ro, key, ri, fs, adr] → [ro, key, ri, fs, adr] flags: <all paths>

Additional information

Used terms: ro, key, ri, fs, adr