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Proof step 30 from proof read-lookup-copy (previous step)

# ax1 = # kx0, # ax0 = # kx, new(ax1, fs), new(ax0, fs), key1 ∈ ri, key ∈ ri, kx0.toSet ⊆ dom ri, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ kx1, fs0, key0, ri0. # kx0 + # kx + 1 = # kx1 ∧ new(ax1, fs0) ∧ ¬ adr ∈ fs0 ∧ new(ax0, fs0) ∧ key0 ∈ ri0 ∧ kx1.toSet ⊆ dom ri0 ∧ (∀ key. key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]])) → fs0[ax1 + adr ' + ax0, fs0[ri0[kx1]]][ri0[kx1, ax1 + adr ' + ax0][key0]] = fs0[ri0[key0]] ∨ dups(kx1) ⊦ fs[ri[key1]] = fs[ri[key]], (ax1 + adr ' + ax0)[# kx0] = adr, dups(kx), dups(kx0), dups(kx0 + kx), dups(ax1 + ax0), dups(ax1), dups(ax0), adr ∈ fs, (ax1 + adr ' + ax0)[# kx0] ∈ ax0, (ax1 + adr ' + ax0)[# kx0] ∈ ax1, key1 ∈ kx, key1 ∈ kx0, key ∈ kx, key ∈ kx0, (ax1 + adr ' + ax0)[# kx0] ∈ fs, adr ∈ ax0, adr ∈ ax1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del, inst: address-list-set name: get-append-grt seq: ⊦ ¬ n < # ax → (ax + ax0)[n] = ax0[n - # ax] subst: [n, ax0, ax] → [# kx0, adr ' + ax0, ax1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m - m = 0; (s)% ⊦ (adr ' + ax)[0] = adr; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ n < # ax → (ax + ax0)[n] = ax[n]; (s)% ⊦ m < # ax → (ax[m] ∈ ax ↔ true); (ss) Used terms: # kx0, adr ' + ax0, ax1