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Proof step 8 from proof delswr (previous step)

∀ r, H, o. r ∈ H ∧ r ∈ rs0 → rs0 = ∅ ∨ H[r, o] \ rs0 = H \ rs0 ∨ # rs0 = 0, r ∈ H, r ∈ rs0 ++ r0 ⊦ rs0 ++ r0 = ∅, H[r, o] \ (rs0 ++ r0) = H \ (rs0 ++ r0), # (rs0 ++ r0) = 0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : diffs-ins, , , ⊦ H0 \ (rs ++ r) = (H0 -- r) \ rs], [CSIMPNAMEDSEQ : write-del, , , r ∈ H ⊦ H[r, o] -- r = H -- r], [CSIMPFORWARD : ⊦ rs ≠ ∅ → # rs ≠ 0], [CSIMPFORWARD : ⊦ # rs ≠ 0 → rs ≠ ∅], [CSIMPFORWARD : ⊦ r ∈ rs → rs ≠ ∅], [CSIMPSEQ : ⊦ r ∈ rs ++ r0 ↔ ¬ ¬ (r = r0 ∨ r ∈ rs)], [CSIMPSEQ : ⊦ ∅ ≠ rs ++ r])]]