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Proof step 11 from proof at-write-at (previous step)

2 + # ax + # ax0 = # ndx, ndx = nd + ndx1, ∀ ax1, ndx0, fs0, adr1. # ax + # ax1 + 1 = # ndx0 → fs0[ax + adr1 ' + ax1, ndx0][adr1] = ndx0[# ax] ∨ dups(ax + ax1) ∨ dups(ax1) ∨ adr1 ∈ ax ∨ adr1 ∈ ax1 ⊦ fs[(adr0 ' + ax) + adr ' + ax0, ndx][adr] = ndx[# ax + 1], adr = adr0, dups(ax0), dups(ax), dups(ax + ax0), adr0 ∈ ax0, adr0 ∈ ax, adr ∈ ax0, adr ∈ ax

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# ndx1 = # ax + # ax0 + 1, ∀ ax1, ndx0, fs0, adr1. # ax + # ax1 + 1 = # ndx0 → fs0[ax + adr1 ' + ax1, ndx0][adr1] = ndx0[# ax] ∨ dups(ax + ax1) ∨ dups(ax1) ∨ adr1 ∈ ax ∨ adr1 ∈ ax1 ⊦ fs[adr0, nd][ax + adr ' + ax0, ndx1][adr] = ndx1[# ax], adr = adr0, dups(ax + ax0), dups(ax), dups(ax0), adr ∈ ax, adr ∈ ax0, adr0 ∈ ax, adr0 ∈ ax0

Rule argument

Additional information

Used simplifier rules: ⊦ (nd ' + ndx)[n + 1] = ndx[n]; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ fs[adr ' + ax, nd ' + ndx] = fs[adr, nd][ax, ndx]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n < n0 ⊦ m + (* n) = m0 + (* n0) ↔ m = m0 + (n0 - n); (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)