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Proof step 4 from proof lookup-02 (previous step)

unique_al(p ' + ax0), a × d ∈ ax0, ∀ a, d. unique_al(ax0) ∧ a × d ∈ ax0 → ax0[a] = d ⊦ (p ' + ax0)[a] = d, a × d = p

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
unique_al(ax0), unique_al(p ' + ax0), a × d ∈ ax0, ∀ a, d. unique_al(ax0) ∧ a × d ∈ ax0 → ax0[a] = d ⊦ (p ' + ax0)[a] = d, a × d = p

Rule argument

fma: unique_al(ax0)

Additional information

Used simplifier rules: not: ⊦ ¬ unique_al(ax) → ¬ unique_al(p ' + ax);% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; Used formulas: unique_al(ax0)