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Proof step 10 from proof at-write-at (previous step)

2 + # ax + # ax0 = # ndx, ∀ 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(ax + ax0), dups(ax), dups(ax0), adr ∈ ax, adr ∈ ax0, adr0 ∈ ax, adr0 ∈ ax0

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
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

Rule argument

var: ndx

Additional information

Used simplifier rules: node-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic