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Proof step 1 from proof ins-two (conclusion)

⊦ a ≠ b → (stng[b, d0][a, d] ≠ stng[a, d][b, d0] ↔ false)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ a = b, stng[b, d0][a, d][a0] = stng[a, d][b, d0][a0]

Rule argument

Additional information

Used simplifier rules: Extension: ⊦ stng1 = stng2 ↔ (∀ a. stng1[a] = stng2[a]);