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Proof step 5 from proof mod-twice (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m ≤ n0, ∀ n, m, n1. n < n0 → (true → m = 0 ∨ (n % m + n1) % m = (n + n1) % m) ⊦ m = 0, ((n0 - m) % m + n1) % m = (n0 + n1) % m

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]