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Proof step 19 from proof lagrange-lemma (previous step)

0 ≤ j0, j0 ^2 |%| j ∈ countFun(0, (j - 1) / 2, λ i. (~1 - i ^2) |%| j), j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ i0 ∈ countFun(i, j, intfun) ↔ (∃ j0. i ≤ j0 ∧ j0 ≤ j ∧ intfun(j0) = i0)
Proof step 21:
0 ≤ j0, ∃ j1. 0 ≤ j1 ∧ j1 ≤ (j - 1) / 2 ∧ (~1 - j1 ^2) |%| j = j0 ^2 |%| j, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Rule argument

spec: intlist inst: name: countFun-in seq: ⊦ i0 ∈ countFun(i, j, intfun) ↔ (∃ j0. i ≤ j0 ∧ j0 ≤ j ∧ intfun(j0) = i0) subst: [intfun, j, i, i0] → [λ i. (~1 - i ^2) |%| j, (j - 1) / 2, 0, j0 ^2 |%| j] flags: rewrite

Additional information

Used terms: λ i. (~1 - i ^2) |%| j, (j - 1) / 2, 0, j0 ^2 |%| j