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Proof step 10 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), ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

User applied rule exists right

And obtained the following new goals

Proof step 11:
ints[m] |%| j = ints[n] |%| j, n < # ints, m < # ints, j < n→i(# ints), 0 < j ⊦ m = n, ints = [], # ints = 1, dups(ints), ints[m] ≠ ints[n] ∧ ≡mod(ints[m], ints[n], j), ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

Rule argument

pos: right 5 terms: ints[m], ints[n] abort: F discard: F computed: F

Additional information

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