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Proof step 19 from proof int2uint-neg (previous step)

true ∈ uint2bits(~ j).rest.rest, j < 0 ⊦ bits2uint(bitsinvert(uint2bits(~ j)) +1) = 2 ^ n→i(# bitsinvert(uint2bits(~ j)) +1) + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
0 < i ⊦ bits2uint(bitsinvert(uint2bits(i)) +1) = 2 ^ n→i(# uint2bits(i)) - i
Proof step 21:
0 < ~ j, true ∈ uint2bits(~ j).rest.rest, j < 0 ⊦ 2 ^ n→i(# uint2bits(~ j)) - ~ j = 2 ^ n→i(# bitsinvert(uint2bits(~ j)) +1) + j

Rule argument

name: uint2uint-inv-01 rotate: F subst: [i] → [~ j]

Additional information

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