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Proof step 37 from proof diff-primes-dups (previous step)

0 ≤ j0, 0 ≤ j, prime(j), j0 ≤ (j - 1) / 2 ⊦ (~1 - j0 ^2) |%| j < j, j = 2, dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j)), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j) + countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
0 ≤ j0, 0 ≤ j, prime(j), j0 ≤ (j - 1) / 2, j ≤ (~1 - j0 ^2) |%| j, 0 ≤ (~1 - j0 ^2) |%| j ⊦ j = 2, dups(countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j)), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j)), dups(countFun(0, (j - 1) / 2, λ i. i ^2 |%| j) + countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j))

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs