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Proof step 63 from proof lagrange-lemma (previous step)

j1 ^2 ≤ ((j - 1) / 2)^2, j0 ^2 ≤ ((j - 1) / 2)^2, 0 ≤ j1, 0 ≤ j, prime(j), j0 ≤ (j - 1) / 2, j1 ≤ (j - 1) / 2, 0 ≤ j0, 0 < j, j ≤ i, 0 < i, 0 ≤ i ⊦ j1 ^2 + j0 ^2 ≤ ((j - 1) / 2)^2 + ((j - 1) / 2)^2, (j1 ^2 + j0 ^2) + 1 ≤ ((j - 1) / 2)^2 + ((j - 1) / 2)^2 + 1, j = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: estimate-add1-le-left seq: ⊦ i + j ≤ j0 ∧ i0 ≤ i → i0 + j ≤ j0 subst: [i, j0, j, i0] → [((j - 1) / 2)^2, ((j - 1) / 2)^2 + ((j - 1) / 2)^2, j0 ^2, j1 ^2] flags: rewrite

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%int-simp-09: ⊦ i ≤ i1 ∧ i2 < i3 → (i1 + i3 ≤ i + i2 ↔ false); from specification int-abs%numle-08: ⊦ i + j ≤ (* i1) * i ↔ j ≤ (i1 - 1) * i; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: ((j - 1) / 2)^2, ((j - 1) / 2)^2 + ((j - 1) / 2)^2, j0 ^2, j1 ^2