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Proof step 15 from proof min-in (previous step)

x1 = i0 + x, ∀ x0. # x0 < # (i + x1) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(i ' + x1) = i, min(i ' + x1) ∈ x1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ min(i ' + j ' + x) = min(min(i, j), min(max(i, j) ' + x))
Proof step 14:
∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(min(i, i0), min(max(i, i0) ' + x)) = i, min(min(i, i0), min(max(i, i0) ' + x)) = i0, min(min(i, i0), min(max(i, i0) ' + x)) ∈ x

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ d ∈ d0 ' + x ↔ d ≠ d0 ∧ ¬ d ∈ x], [CSIMPSEQ : ⊦ min(i, j) = min(j, i)], [CSIMPSEQ : ⊦ min(i, min(j, j0)) = min(min(i, j), j0)], [CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d + x = d ' + x])]]