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Proof step 8 from proof subset-uni (previous step)

H0 ⊆ H1, H1 \ H0 ⊥ H0 ⊦ ∀ r. (r ∈ (H1 \ H0) ∪ H0 ↔ r ∈ H1) ∧ (r ∈ (H1 \ H0) ∪ H0 → ((H1 \ H0) ∪ H0)[r] = H1[r])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
H0 ⊆ H1, H1 \ H0 ⊥ H0, r ∈ H1 ∨ r ∈ H0 ⊦ ((H1 \ H0) ∪ H0)[r] = H1[r]

Rule argument

Additional information

Used simplifier rules: in-uni: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1);%diff-in: ⊦ r ∈ H0 \ H1 ↔ r ∈ H0 ∧ ¬ r ∈ H1;%subset-in: ⊦ H0 ⊆ H1 ∧ r ∈ H0 → r ∈ H1;