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Proof step 7 from proof cast-mod-ls-pos (previous step)

i→n(i) < # int2bits(j), 0 < i, j < 2 ^ (i - 1), 0 ≤ j ⊦ bits2int(lastn(i→n(i), int2bits(j))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1))

Rule argument

seq: ⊦ 0 < i → (m < # int2bits(i) ↔ ¬ i < 2 ^ (n→i(m) - 1)) subst: [i, m] → [j, i→n(i)] rotate: F spec: int2bits inst: name: int2bits-lslen-06

Additional information

Used simplifier rules: ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ int2bits(0) = false ';% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ # boolvar ' = 0 +1;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;%0 ≤ i ⊦ i→n(i) < (* m) ↔ i < n→i(m);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j, i→n(i)