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Proof step 12 from proof mapex-new (previous step)

⊦ ((r => f(r) * P))((mk(rs, f) ++ r)[r, f(r)]) ↔ ((r => f(r) * P))(mk(rs ++ r, f)[r, f(r)]), r = null, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ((r => o * P))(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = o
Proof step 14:
⊦ P((mk(rs, f) ++ r)[r, f(r)] -- r) ∧ r ∈ (mk(rs, f) ++ r)[r, f(r)] ∧ (mk(rs, f) ++ r)[r, f(r)][r] = f(r) ↔ ((r => f(r) * P))(mk(rs ++ r, f)[r, f(r)]), r = null, r ∈ rs

Rule argument

spec: maplet name: map-del seq: ⊦ ((r => o * P))(H) ↔ P(H -- r) ∧ r ∈ H ∧ H[r] = o subst: [H, P, o, r] → [(mk(rs, f) ++ r)[r, f(r)], P, f(r), r] flags: <all paths>

Additional information

Used terms: (mk(rs, f) ++ r)[r, f(r)], P, f(r), r