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Proof step 24 from proof int2int-inj (previous step)

uint2bits(~ i) = false ' + true ' + bits, i < 0 ⊦ 2 ^ n→i(# bits) + i = 0, true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ ¬ true ∈ bits ∧ 0 ≤ i → (uint2bits(i) = false ' + true ' + bits ↔ i = 2 ^ n→i(# bits))

Rule argument

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

Additional information

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