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

∀ a, ay. a ∈ ax0 → (ax0 + ay)[a] = ax0[a] ⊦ ((p ' + ax0) + ay)[a] = (p ' + ax0)[a], ¬ a ∈ p ' ∧ ¬ a ∈ ax0

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a ∈ p ', ∀ a, ay. a ∈ ax0 → (ax0 + ay)[a] = ax0[a] ⊦ ((p ' + ax0) + ay)[a] = (p ' + ax0)[a], ¬ a ∈ p ' ∧ ¬ a ∈ ax0
Proof step 7:
∀ a, ay. a ∈ ax0 → (ax0 + ay)[a] = ax0[a] ⊦ a ∈ p ', ((p ' + ax0) + ay)[a] = (p ' + ax0)[a], ¬ a ∈ p ' ∧ ¬ a ∈ ax0

Rule argument

fma: a ∈ p '

Additional information

Used formulas: a ∈ p '