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Proof step 25 from proof del-put-switch (previous step)

⊦ r = r0, ∀ rk. (rk ∈ st[r -- sk, val] -- r0 ↔ rk ∈ (st -- r0)[r -- sk, val]) ∧ (st[r -- sk, val] -- r0)[rk] = ((st -- r0)[r -- sk, val][rk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
⊦ r = r0, (rk ∈ st[r -- sk, val] -- r0 ↔ rk = r -- sk ∨ rk ∈ st -- r0) ∧ (st[r -- sk, val] -- r0)[rk] = ((rk = r -- sk ⊃ val; (st -- r0)[rk]))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st])]]