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Proof step 2 from proof int2bits-lslen-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < ~1 ∧ 0 ≤ j → (0 ≤ 2 ^ j + i ↔ # int2bits(i) ≤ i→n(j) + 1)
Proof step 4:
i < ~1 ∧ 0 ≤ n→i(m) - 1, i < ~1, i < 0 ⊦ m < # int2bits(i) ↔ ¬ # int2bits(i) ≤ i→n(n→i(m) - 1) + 1

Rule argument

name: int2bits-lslen-02 rotate: F subst: [i, j] → [i, n→i(m) - 1]

Additional information

Used simplifier rules: int2bits-neg-num: i < 0 ⊦ int2bits((* i)) = sgn(bitsinvert(uint2bits(abs(i))) +1);%uint2bits-one: ⊦ uint2bits(1) = false + true;%int2bits-not-empty: ⊦ int2bits(j) ≠ [];% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ 0 < n ↔ n ≠ 0;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bitsinvert(true ') = false ';% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + false ')+1 = bits + true;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ sgn(true ' + true ') = true ';% ⊦ # boolvar ' = 0 +1;% ⊦ m < 1 ↔ m = 0;% ⊦ i + ~1 = i - 1;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ # bits = 0 ↔ bits = [];% ⊦ i + 0 = i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j = j + i; Used terms: i, n→i(m) - 1