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Proof step 7 from proof int2bits-lelen-06 (previous step)

2 < # int2bits(i), 2 < m, m ≤ i→n(n→i(m) - 2) + 1, 0 < i, m ≤ # int2bits(i), # int2bits(i) ≤ i→n(n→i(m) - 2) + 1 ⊦ m = 3, m = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j)
Proof step 9:
2 ≤ n→i(m) ∧ 0 ≤ 2, 2 < # int2bits(i), 2 < m, m ≤ (i→n(n→i(m)) - i→n(2)) + 1, 0 < i, m ≤ # int2bits(i), # int2bits(i) ≤ (i→n(n→i(m)) - i→n(2)) + 1 ⊦ m = 3, m = 2

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: num-n2i-ls-06: 0 ≤ i ⊦ (* i) ≤ n→i(n) ↔ i→n(i) ≤ n; from specification intnat%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: 2, n→i(m)