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Proof step 2 from proof index-lookup-app (previous step)

∀ ri, kx1. ri[kx + kx1] = ri[kx] + ri[kx1] ⊦ ri[(key + kx) + kx1] = ri[key + kx] + ri[kx1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: index-lookup-rec: ⊦ ri[key ' + kx] = ri[key] + ri[kx];% ⊦ adr ' + ax = adr ' + ax0 ↔ ax = ax0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr + ax = adr ' + ax; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ key + kx = key ' + kx; (s)