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Proof step 1 from proof Data-in-putdelput (conclusion)

⊦ ¬ d0 ∈ st ∧ d0 ≠ d1 ∧ d0 ≠ d2 → ¬ d0 ∈ (st[b, d1] -- a)[c, d2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a0 ∈ (st[b, d1] -- a)[c, d2] ⊦ (st[b, d1] -- a)[c, d2][a0] = d1, (st[b, d1] -- a)[c, d2][a0] = d2, ∃ a1. a1 ∈ st ∧ st[a1] = (st[b, d1] -- a)[c, d2][a0]

Rule argument

Additional information

Used simplifier rules: Data-in: ⊦ d ∈ st ↔ (∃ a. a ∈ st ∧ st[a] = d);