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Proof step 9 from proof replay-log-gc-copy (previous step)

# ax0 = # kx1, # ax0 = # fs[ri[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 → replay-log(ax0, fs0[ax0, fs0[ri0[kx0]]], ri0 ⊖ ro0) = ri0[kx0, ax0] ⊖ ro0 ∨ dups(kx0) ⊦ replay-log(ax0, fs[ax0, fs[ri[kx1]]][adr, fs[ri[key]]], replay-one(adr, fs[ax0, fs[ri[kx1]]][adr, fs[ri[key]]][adr], ri ⊖ ro)) = ri[key, adr][kx1, ax0] ⊖ ro, dups(kx1), dups(ax0), key ∈ kx1, adr ∈ fs, adr ∈ ax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# 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 → replay-log(ax0, fs0[ax0, fs0[ri0[kx0]]], ri0 ⊖ ro0) = ri0[kx0, ax0] ⊖ ro0 ∨ dups(kx0) ⊦ replay-log(ax0, fs[ax0, fs[ri[kx1]]], replay-one(adr, fs[ri[key]], ri ⊖ ro)) = ri[key, adr][kx1, ax0] ⊖ ro, dups(ax0), dups(kx1), adr ∈ ax0, adr ∈ fs, key ∈ kx1

Rule argument

Additional information

Used simplifier rules: replay-log-write: ⊦ ¬ adr ∈ log → replay-log(log, fs[adr, nd], ri) = replay-log(log, fs, ri);% ⊦ fs[adr, nd][adr] = nd; (s)% ⊦ # ri[kx] = # kx; (s)% ⊦ # fs[ax] = # ax; (s)