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Proof step 14 from proof ri-cons-copy-new (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Rule argument

var: ax0

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # kx = 0 ↔ kx = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic