[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 8 from proof int2uint-neg (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
0 < i ⊦ ∃ bits. uint2bits(i) = false ' + true ' + bits
Proof step 10:
∃ bits. uint2bits(~ j) = false ' + true ' + bits, j < 0 ⊦ bits2uint(sgn(bitsinvert(uint2bits(~ j)) +1)) = 2 ^ n→i(# sgn(bitsinvert(uint2bits(~ j)) +1)) + j, true ∈ uint2bits(~ j).rest.rest

Rule argument

name: uint2bits-expos0 subst: [i] → [~ j]

Additional information

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