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Proof step 3 from proof index-update-dom (previous step)

# kx0 + 1 = # ax, ∀ ax, ri. # kx0 = # ax → dom ri[kx0, ax] = dom ri ∪ kx0.toSet ⊦ dom ri[key ' + kx0, ax] = (kx0.toSet ∪ dom ri) ++ key

User applied rule constructor cut

And obtained the following new goals

Proof step 4:
# kx0 + 1 = # ax, ax = adr + ax0, ∀ ax, ri. # kx0 = # ax → dom ri[kx0, ax] = dom ri ∪ kx0.toSet ⊦ dom ri[key ' + kx0, ax] = (kx0.toSet ∪ dom ri) ++ key

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