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Proof step 1 from proof min-delmin (conclusion)

⊦ 1 < # s → s.min < (s -- s.min).min

User applied rule simplifier

And obtained the following new goals

Proof step 2:
s.min ∈ s, s.max ∈ s ⊦ s = ∅, # s = 0, # s = 1, s.min < (s -- s.min).min

Rule argument

Additional information

Used simplifier rules: Max-in: ⊦ s ≠ ∅ → s.max ∈ s;%Min-in: ⊦ s ≠ ∅ → s.min ∈ s;%Max-max: ⊦ a ∈ s → ¬ s.max < a;%Min-min: ⊦ a ∈ s → ¬ a < s.min;%minmax-04: ⊦ s ≠ ∅ → ¬ s.max < s.min;%irreflexivity: ⊦ ¬ a < a; from specification oelem%size-zero-01: ⊦ s ≠ ∅ → # s ≠ 0; (forward) from specification set-basic%size-zero: ⊦ # s ≠ 0 → s ≠ ∅; (forward) from specification set-basic%one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1