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Proof step 5 from proof write-app (previous step)

# ax1 = # ndx1, # ax + 1 = # ndx0, ndx0 = nd + ndx, ∀ ax1, ndx1, ndx0, fs. # ax1 = # ndx1 ∧ # ax = # ndx0 → fs[ax + ax1, ndx0 + ndx1] = fs[ax, ndx0][ax1, ndx1] ⊦ fs[(adr ' + ax) + ax1, ndx0 + ndx1] = fs[adr ' + ax, ndx0][ax1, ndx1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# ax1 = # ndx1, # ax = # ndx, ∀ ax1, ndx1, ndx0, fs. # ax1 = # ndx1 ∧ # ndx = # ndx0 → fs[ax + ax1, ndx0 + ndx1] = fs[ax, ndx0][ax1, ndx1] ⊦ fs[adr, nd][ax + ax1, ndx + ndx1] = fs[adr, nd][ax, ndx][ax1, ndx1]

Rule argument

Additional information

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