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Proof step 4 from proof dec-int (previous step)

0 ≤ i ⊦ decode(2 * i→n(i)) = i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pair inst: name: dec-int-pos seq: ⊦ n % 2 = 0 → decode(n) = n→i(n / 2) subst: [n] → [2 * i→n(i)] flags: rewrite, current

Additional information

Used simplifier rules: dec-int-neg: ⊦ n % 2 ≠ 0 → decode(n) = ~ n→i((n + 1) / 2);%mod-mult-01: n ≠ 0 ⊦ (m * n) % n = 0; from specification nat-div%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%two-mdiv2-02: ⊦ (2 * m) / 2 = m; from specification nat-div%i2i-pos-01: ⊦ 0 ≤ i → n→i(i→n(i)) = i; from specification intnat%two-mdiv2-03: ⊦ (2 * m + 1) / 2 = m; from specification nat-div%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%negeq: ⊦ ~ i = j ↔ i + j = 0; from specification int-abs%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%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); 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: 2 * i→n(i)