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Proof step 5 from proof index-update-adr-in (previous step)

# kx0 + 1 = # ax, ∀ ax0, adr0, ri0. # kx0 = # ax0 → (adr0 ∈ ri0[kx0, ax0] ↔ adr0 ∈ ax0 ∨ adr0 ∈ ri0 \ kx0.toSet) ⊦ adr ∈ ri[key ' + kx0, ax] ↔ adr ∈ ax ∨ adr ∈ ri \ (kx0.toSet ++ key), dups(kx0), key ∈ kx0

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
# kx0 + 1 = # ax, ax = adr1 + ax1, ∀ ax0, adr0, ri0. # kx0 = # ax0 → (adr0 ∈ ri0[kx0, ax0] ↔ adr0 ∈ ax0 ∨ adr0 ∈ ri0 \ kx0.toSet) ⊦ adr ∈ ri[key ' + kx0, ax] ↔ adr ∈ ax ∨ adr ∈ ri \ (kx0.toSet ++ key), dups(kx0), key ∈ kx0

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