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Proof step 9 from proof log-cons-copy-new (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Rule argument

var: kx0

Additional information

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