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Proof step 12 from proof int2bits-lelen-06 (previous step)

i→n(n→i(m) - 2) + 1 < m, i→n(n→i(m) - 2) + 1 < # int2bits(i), # int2bits(i) < m, 2 ≤ m, 0 < i, 2 + i→n(n→i(m) - 2) < m ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j)

Rule argument

spec: intnat inst: name: sub seq: j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j) subst: [j, i] → [2, n→i(m)] flags: rewrite

Additional information

Used simplifier rules: le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%num-n2i-ls-06: 0 ≤ i ⊦ (* i) ≤ n→i(n) ↔ i→n(i) ≤ n; from specification intnat%n2n: ⊦ i→n(n→i(n)) = n; from specification intnat%sub-ls: ⊦ ¬ n + (m - n) < m; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: 2, n→i(m)