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Proof step 2 from proof read-length (previous step)

∀ fs. # fs[ax0] = # ax0 ⊦ # fs[adr + ax0] = #(adr + ax0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ fs. # fs[ax0] = # ax0 ⊦ # fs[ax0] = # ax0

Rule argument

Additional information

Used simplifier rules: read-rec: ⊦ fs[adr ' + ax] = fs[adr] + fs[ax];%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)% ⊦ #(adr ' + ax) = (# ax)+1; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ m +1 = m + 1; (s)% ⊦ #(nd ' + ndx) = (# ndx)+1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ nd + ndx = nd ' + ndx; (s)% ⊦ adr + ax = adr ' + ax; (s)