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Proof step 1 from proof ls-06 (conclusion)

⊦ n ≤ m → (m - n < m ↔ n ≠ 0)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: sub-base: ⊦ m - 0 = m;%lels-01: ⊦ ¬ m ≤ n ↔ n < m;%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false);%ls-01: n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0;%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%l-01: ⊦ m < m + n ↔ n ≠ 0; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1