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Proof step 2 from proof map-putrev (previous step)

r ∈ rs ⊦ # rs = 0, ((r => o0 * P))(mk(rs, f)[r, o1]) ↔ o0 = o1 ∧ ((r =>_ * P))(mk(rs, f)), rs = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
r ∈ H ⊦ ((r => o0 * P))(H[r, o1]) ↔ o0 = o1 ∧ ((r =>_ * P))(H)

Rule argument

spec: maplet name: map-putex seq: r ∈ H ⊦ ((r => o0 * P))(H[r, o1]) ↔ o0 = o1 ∧ ((r =>_ * P))(H) subst: [o1, H, P, o0, r] → [o1, mk(rs, f), P, o0, r] flags: <all paths>

Additional information

Used simplifier rules: in-mk: ⊦ r ∈ mk(rs, f) ↔ r ∈ rs; Used terms: o1, mk(rs, f), P, o0, r