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Proof step 12 from proof range-cong-dups (previous step)

ints[m] |%| j = ints[n] |%| j, n < # ints, m < # ints, j < n→i(# ints), 0 < j ⊦ m = n, ints = [], # ints = 1, dups(ints), ≡mod(ints[m], ints[n], j), ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mod inst: name: congmod-def-mod seq: ⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j) subst: [j, i0, i] → [j, ints[n], ints[m]] flags: rewrite, current

Additional information

Used terms: j, ints[n], ints[m]