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Proof step 22 from proof mapex-new (previous step)

r0 ∈ rs ⊦ # rs = 0, P(mk(rs, f)) ↔ P(mk(rs ++ r, f) -- r), (mk(rs ++ r, f) -- r)[r0] = f(r0), r = null, rs = ∅, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
r ∈ H ⊦ r ≠ r0 → (H -- r0)[r] = H[r]
Proof step 24:
r0 ∈ rs, r0 ∈ mk(rs ++ r, f) ⊦ # rs = 0, P(mk(rs, f)) ↔ P(mk(rs ++ r, f) -- r), mk(rs ++ r, f)[r0] = f(r0), r = null, r0 = r, rs = ∅, r ∈ rs

Rule argument

spec: heap name: at-del seq: r ∈ H ⊦ r ≠ r0 → (H -- r0)[r] = H[r] subst: [r, r0, H] → [r0, r, mk(rs ++ r, f)] flags: <all paths>

Additional information

Used simplifier rules: in-mk: ⊦ r ∈ mk(rs, f) ↔ r ∈ rs;% ⊦ r ≠ r0 → (r ∈ rs ++ r0 ↔ r ∈ rs); (s) Used terms: r0, r, mk(rs ++ r, f)