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Proof step 6 from proof mod-twice (previous step)

∀ n, m, n1. n < n0 → (true → m = 0 ∨ (n % m + n1) % m = (n + n1) % m) ⊦ (n0 % m + n1) % m = (n0 + n1) % m, m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
n ≠ 0 ⊦ n ≤ m → m % n = (m - n) % n
Proof step 5:
m ≠ 0 ∧ m ≤ n0, ∀ n, m, n1. n < n0 → (true → m = 0 ∨ (n % m + n1) % m = (n + n1) % m) ⊦ ((n0 - m) % m + n1) % m = (n0 + n1) % m, m = 0

Rule argument

[x0lemmaarg: spec-name: nat-div instance-name: lemma-name: mod-rec antecedent: n ≠ 0 succedent: n ≤ m → m % n = (m - n) % n substlist: [n, m] → [m, n0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < n → m % n = m])], [EXTRATERMS : (m, n0)]]