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Proof step 16 from proof int2bits-len-neg (previous step)

uint2bits(~ j) = false ' + true ' + bits, j + 1 < 2 ^ i, j < i, 0 < 2 ^ i, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, j + 2 ^ i < 0, j + 2 ^ i < i, j < ~1, j < 0, j < 2 ^ i ⊦ bits = [], # bits = 1 + i→n(i), true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ¬ true ∈ bits ∧ 0 ≤ i → (uint2bits(i) = false ' + true ' + bits ↔ i = 2 ^ n→i(# bits))
Proof step 18:
¬ true ∈ bits ∧ 0 ≤ ~ j, ~ j = 2 ^ n→i(# bits), j + 1 < 2 ^ i, j < i, 0 < 2 ^ i, 0 ≤ i, 0 ≤ 2 ^ i * 2 + j, j + 2 ^ i < 0, j + 2 ^ i < i, j < ~1, j < 0, j < 2 ^ i ⊦ bits = [], # bits = 1 + i→n(i), true ∈ bits

Rule argument

name: uint2bits-2pot-03 rotate: F subst: [bits, i] → [bits, ~ j]

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + 0 = i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: bits, ~ j