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Proof step 1 from proof subdef (conclusion)

⊦ s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 2:
⊦ s1 ⊆ s2, s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2)

Rule argument

fma: s1 ⊆ s2

Additional information

Used simplifier rules: sub-in: ⊦ a ∈ s ∧ s ⊆ s0 → a ∈ s0; (forward) from specification set-basic%ne-01: ⊦ a ∈ s → s ≠ ∅; (forward) from specification set-basic Used formulas: s1 ⊆ s2