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Proof step 30 from proof cont-monotone (previous step)

∃ n. (n = 0 ⊃ S0;S)(x0), f(S0)(x), S0 ⊆ S, f(λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0))(x) ⊦ S(x0), f(S)(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information