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Proof step 26 from proof cont-monotone (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 27:
(λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0)) = S, f(S0)(x), S0 ⊆ S, f(λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0))(x) ⊦ f(S)(x)
Proof step 28:
f(S0)(x), S0 ⊆ S, f(λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0))(x) ⊦ (λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0)) = S, f(S)(x)

Rule argument

fma: (λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0)) = S

Additional information

Used formulas: (λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0)) = S