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Proof step 5 from proof update-index-append (previous step)

# kx1 = # ax1, # kx + 1 = # ax0, ax0 = adr + ax, ∀ 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# kx1 = # ax1, # kx = # ax, ∀ kx1, ax1, ax0, ri. # kx1 = # ax1 ∧ # ax = # ax0 → ri[kx + kx1, ax0 + ax1] = ri[kx, ax0][kx1, ax1] ⊦ ri[key, adr][kx + kx1, ax + ax1] = ri[key, adr][kx, ax][kx1, ax1]

Rule argument

Additional information

Used simplifier rules: index-update-key-rec: ⊦ ri[key ' + kx, adr ' + ax] = ri[key, adr][kx, ax];%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)% ⊦ adr + ax = adr ' + ax; (s)