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Proof step 4 from proof max-ge (previous step)

i ∈ x, i0 < i, max(i1 ' + x) < i, i1 ≤ i0, i1 < i, ∀ x0, i. # x0 < # (i0 + i1 + x) → (i ∈ x0 ∧ max(x0) < i → false) ⊦ i = i0

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [x0, i] → [i1 ' + x, i]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ y → d ∈ x + y], [CSIMPSEQ : ⊦ # (x + y) = # x + # y], [CSIMPSEQ : ⊦ # d ' = 0 +1], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d + x = d ' + x], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (i1 ' + x, i)]]