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Proof step 10 from proof uint2bits-sgn-2pot (previous step)

bits2uint(uint2bits(j)) = bits2uint(false ' + true ' + bits), uint2bits(j) = false ' + true ' + bits, 0 < j, ∀ i. ¬ i < 0 → j ≠ 2 ^ i ⊦ sgn(true ' + bits) = true ' + true ' + bits, true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 ≤ i → bits2uint(uint2bits(i)) = i
Proof step 12:
0 ≤ j, j = bits2uint(false ' + true ' + bits), uint2bits(j) = false ' + true ' + bits, 0 < j, ∀ i. ¬ i < 0 → j ≠ 2 ^ i ⊦ sgn(true ' + bits) = true ' + true ' + bits, true ∈ bits

Rule argument

name: uint2uint-pos rotate: F subst: [i] → [j]

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: j