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Proof step 12 from proof cont-monotone (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ chain(Sn) ↔ (∀ m, n. Sn(m) ⊆ Sn(n) ∨ Sn(n) ⊆ Sn(m))
Proof step 14:
f(S0)(x), S0 ⊆ S ⊦ ∀ m, n. (m = 0 ⊃ S0;S) ⊆ (n = 0 ⊃ S0;S) ∨ (n = 0 ⊃ S0;S) ⊆ (m = 0 ⊃ S0;S), f(S)(x)

Rule argument

spec: inst: name: chain-def seq: ⊦ chain(Sn) ↔ (∀ m, n. Sn(m) ⊆ Sn(n) ∨ Sn(n) ⊆ Sn(m)) subst: [Sn] → [λ n. (n = 0 ⊃ S0;S)] flags: rewrite, current

Additional information

Used terms: λ n. (n = 0 ⊃ S0;S)