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Proof step 8 from proof mk-exists (previous step)

∀ H0. # H0 < # H → true → (∃ rs, f. H0 = mk(rs, f)) ⊦ ∀ r. (r ∈ H ↔ r ∈ ∅) ∧ (r ∈ H → H[r] = (∅)[r]), ∃ rs, f. H = mk(rs, f)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
r ∈ H, ∀ H0. # H0 < # H → true → (∃ rs, f. H0 = mk(rs, f)) ⊦ ∃ rs, f. H = mk(rs, f)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ r ∈ ∅; (s)