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Proof step 17 from proof min-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
∀ x0. # x0 < # (i + x1) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(i ' + x1) = i, min(i ' + x1) ∈ x1

Rule argument

[emptyarg]

Additional information

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