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Proof step 6 from proof map-in0 (previous step)

((r => o))(mk(rs, f)) ⊦ mk(rs, f) = (∅ ++ r)[r, o], r = null, r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null

Rule argument

spec: maplet name: maplet seq: ⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null subst: [H, o, r] → [mk(rs, f), o, r] flags: <all paths>

Additional information

Used terms: mk(rs, f), o, r