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Proof step 16 from proof ri-cons-copy-new (previous step)

# ax1 = # kx1, # kx0 = # ax, new(ax1, fs), new(ax, fs), key ∈ ri, kx1.toSet ⊆ dom ri, kx0.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(kx0), dups(kx1), dups(kx1 + kx0), dups(ax1 + ax), dups(ax1), dups(ax), adr ∈ fs, key ∈ kx0, key ∈ kx1, adr ∈ ax, adr ∈ ax1, ( (ax1 + adr ' + ax)[# kx1] ∈ fs ∨ (ax1 + adr ' + ax)[# kx1] ∈ ax1 ∨ (ax1 + adr ' + ax)[# kx1] = adr ∨ (ax1 + adr ' + ax)[# kx1] ∈ ax) ∧ key-cons(key, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key]]][ax, fs[ri[kx0]]][(ax1 + adr ' + ax)[# kx1]])

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] → [# kx1, adr ' + ax, ax1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n < # ax → (ax + ax0)[n] = ax[n]; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ m < # ax → (ax[m] ∈ ax ↔ true); (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ # kx = 0 ↔ kx = []; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: # kx1, adr ' + ax, ax1