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Proof step 5 from proof ri-closed-gc (previous step)

# kx0 + 1 = # ax, new(ax, fs), ri-closed(ri, fs, ro), ri-cons(ri, fs), key ∈ ri, kx0.toSet ⊆ dom ri, ∀ ax0, fs0, ri0, ro0. # kx0 = # ax0 ∧ new(ax0, fs0) ∧ ri-closed(ri0, fs0, ro0) ∧ ri-cons(ri0, fs0) ∧ kx0.toSet ⊆ dom ri0 → dups(ax0) ∨ ri-closed(ri0[kx0, ax0], fs0[ax0, fs0[ri0[kx0]]], ro0) ⊦ dups(ax), dups(kx0), ri-closed(ri[key ' + kx0, ax], fs[ax, fs[ri[key]] ' + fs[ri[kx0]]], ro), key ∈ kx0

User applied rule constructor cut

And obtained the following new goals

Rule argument

var: ax

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