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Proof step 30 from proof int2int-inj (previous step)

uint2bits(~ i) = false ' + true ' + bits, true ∈ bits, i < 0, true ∈ bitsinvert(bits) +1 ⊦ bits2uint(uint2bits(~ i)) + i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ 0 ≤ i → bits2uint(uint2bits(i)) = i

Rule argument

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

Additional information

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