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Proof step 5 from proof update-index-data-notin (previous step)

# kx0 + 1 = # ax, adr ∈ ri[key ' + kx0, ax], ∀ ax, adr, ri. # kx0 = # ax ∧ adr ∈ ri[kx0, ax] → adr ∈ ax ∨ adr ∈ ri ⊦ adr ∈ ax, adr ∈ ri

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
# kx0 + 1 = # ax, ax = adr0 + ax0, adr ∈ ri[key ' + kx0, ax], ∀ ax, adr, ri. # kx0 = # ax ∧ adr ∈ ri[kx0, ax] → adr ∈ ax ∨ adr ∈ ri ⊦ adr ∈ ri, adr ∈ ax

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