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Proof step 4 from proof read-split (previous step)

fs[adr] ' + fs[ax0] = ndx0 + ndx1, ∀ fs, ndx0, ndx1. fs[ax0] = ndx0 + ndx1 → (∃ ax2, ax1. ax0 = ax2 + ax1 ∧ fs[ax2] = ndx0 ∧ fs[ax1] = ndx1), fs[adr] ∈ ndx0 ∨ fs[adr] ∈ ndx1 ⊦ ∃ ax, ax1. adr ' + ax0 = ax + ax1 ∧ fs[ax] = ndx0 ∧ fs[ax1] = ndx1

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
fs[adr] ' + fs[ax0] = ndx0 + ndx1, fs[adr] ∈ ndx0, ∀ fs, ndx0, ndx1. fs[ax0] = ndx0 + ndx1 → (∃ ax2, ax1. ax0 = ax2 + ax1 ∧ fs[ax2] = ndx0 ∧ fs[ax1] = ndx1), fs[adr] ∈ ndx0 ∨ fs[adr] ∈ ndx1 ⊦ ∃ ax, ax1. adr ' + ax0 = ax + ax1 ∧ fs[ax] = ndx0 ∧ fs[ax1] = ndx1

Rule argument

fma: fs[adr] ∈ ndx0

Additional information

Used simplifier rules: read-eq-empty: ⊦ fs[ax] = [] ↔ ax = [];%read-rec: ⊦ fs[adr ' + ax] = fs[adr] + fs[ax];%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ nd ' + ndx = ndx0 + ndx1 → (nd ∈ ndx0 ↔ ndx0 ≠ []); (ss)% ⊦ [] + ndx = ndx; (s)% ⊦ ¬ nd ∈ []; (s)% ⊦ [] + ax = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ nd + ndx = nd ' + ndx; (s) Used formulas: fs[adr] ∈ ndx0