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Proof step 3 from proof alignup-is-even-bigger (conclusion)

m ≠ 0, n1 ≤ n0 ⊦ ¬ align↑(n0, m) + n2 < n1

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: alignup-is-bigger seq: m ≠ 0 ⊦ n0 ≤ align↑(n0, m) subst: [m, n0] → [m, n0] flags: current, []

Additional information

[Concretesimprules((Csimpnamedseq(alignup-def,,, 0 ≠ m ⊦ align↑(n, m) = (n % m = 0 ⊃ n;(n / m)+1 * m)) Csimpnamedseq(nat-basic2,,succ, ⊦ m +1 = m + 1) Csimpnamedseq(nat-mult,,rsucc-02, ⊦ m * (n + 1) = m * n + m) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(nat-mult,,mult-a, ⊦ m0 * m * n = (m0 * m) * n) Csimpnamedseq(nat-mult,,mult-c, ⊦ m * n = n * m) Csimpnamedforward(nat,,fle, ⊦ m < n ∧ n ≤ n0 → m < n0) Csimpnamedforward(nat-basic1,,f, ⊦ m < n → n ≠ 0) Csimpnamedforward(nat,,let, ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1) Csimpnamedseq(nat-basic2,,l-02, ⊦ ¬ m + n < m))), Extraterms((mn0))]