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Proof step 11 from proof Del-at (previous step)

b = a0, ∀ b, a. (st0 -- b)[a] = st0[a] ∨ a = b ⊦ (st0[a0, d] -- b)[a] = st0[a], a = b, a = a0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
∀ b, a. (st0 -- b)[a] = st0[a] ∨ a = b ⊦ (st0 -- a0)[a] = st0[a], a = a0

Rule argument

Additional information

Used simplifier rules: Del-rec-same: ⊦ st[a, d] -- a = st -- a;