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Proof step 4 from proof min-le (previous step)

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

User applied rule apply induction

And closed the goal!

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ d + x = d ' + x], [CSIMPSEQ : ⊦ # d ' = 0 +1], [CSIMPSEQ : ⊦ # (x + y) = # x + # y], [CSIMPSEQ : ⊦ d ≠ d0 → (d ∈ d0 ' + x ↔ d ∈ x)], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ ¬ i < min(i, j)], [CSIMPSEQ : ⊦ min(i, min(j, j0)) = min(min(i, j), j0)], [CSIMPSEQ : ⊦ min(i, j) = min(j, i)])], [EXTRATERMS : (i1 ' + x, i)]]