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Proof step 4 from proof write-app (previous step)

# ax1 = # ndx1, # ax + 1 = # ndx0, ∀ 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]

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
# 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]

Rule argument

var: ndx0

Additional information

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