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Proof step 8 from proof map-in0 (previous step)

((r => o))(mk(rs, f)), ∀ r. r ∈ rs → g(r) = a ⊦ r ∈ rs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ((r => o))(H) ↔ H = (∅ ++ r)[r, o] ∧ r ≠ null
Proof step 10:
mk(rs, f) = (∅ ++ r)[r, o], ∀ r. r ∈ rs → g(r) = a ⊦ r = null, r ∈ rs

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