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Proof step 1 from proof map-putrev (conclusion)

r ∈ rs ⊦ (r => o0 * P)[rs, f(r; o1)] ↔ o0 = o1 ∧ (r =>_ * P)[rs, f]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
r ∈ rs ⊦ # rs = 0, ((r => o0 * P))(mk(rs, f)[r, o1]) ↔ o0 = o1 ∧ ((r =>_ * P))(mk(rs, f)), rs = ∅

Rule argument

Additional information

Used simplifier rules: apply: ⊦ P[rs, f] ↔ P(mk(rs, f));%write: ⊦ r ∈ rs → mk(rs, f(r; o)) = mk(rs, f)[r, o];%size-zero-01: ⊦ rs ≠ ∅ → # rs ≠ 0; (forward) from specification set-basic[refset]%ne-01: ⊦ r ∈ rs → rs ≠ ∅; (forward) from specification set-basic[refset]