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Proof step 4 from proof update-index-append (previous step)

# kx1 = # ax1, # kx + 1 = # ax0, ∀ kx1, ax1, ax0, ri. # kx1 = # ax1 ∧ # kx = # ax0 → ri[kx + kx1, ax0 + ax1] = ri[kx, ax0][kx1, ax1] ⊦ ri[(key ' + kx) + kx1, ax0 + ax1] = ri[key ' + kx, ax0][kx1, ax1]

User applied rule constructor cut

And obtained the following new goals

Rule argument

var: ax0

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