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Proof step 37 from proof int2bits-neg-03 (previous step)

~1 = (2 ^ n→i(# int2bits(~ j)) + j) % 2, 2 ^ n→i(# int2bits(~ j)) + j < 0, j < 0 ⊦ ~1 = 2 ^ n→i(# int2bits(~ j)) + j, true ∈ uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ 0 < j → true ∈ uint2bits(j)

Rule argument

name: uint2bits-onein rotate: F subst: [j] → [~((2 ^ n→i(# int2bits(~ j)) + j) / 2)]

Additional information

Used simplifier rules: ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); Used terms: ~((2 ^ n→i(# int2bits(~ j)) + j) / 2)