[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 22 from proof int2int-neg (previous step)

j < 2 ^ n→i(# int2bits(~ j)), 1 < 2 ^ n→i(# int2bits(~ j)), j < 0, 0 < 2 ^ n→i(# int2bits(~ j)) + j, 0 ≤ 2 ^ n→i(# int2bits(~ j)) + j, 0 ≤ 2 ^ n→i(# int2bits(~ j)), 0 < 2 ^ n→i(# int2bits(~ j)), j + 1 < 2 ^ n→i(# int2bits(~ j)) ⊦ 2 ^ n→i(# int2bits(~ j)) = 2 ^ (n→i(# uint2bits(2 ^ n→i(# int2bits(~ j)) + j)) - 1)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 23:
⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1))
Proof step 24:
0 < ~ j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ ~ j ∧ ~ j < 2 ^ (i + 1)), j < 2 ^ n→i(# int2bits(~ j)), 1 < 2 ^ n→i(# int2bits(~ j)), j < 0, 0 < 2 ^ n→i(# int2bits(~ j)) + j, 0 ≤ 2 ^ n→i(# int2bits(~ j)) + j, 0 ≤ 2 ^ n→i(# int2bits(~ j)), 0 < 2 ^ n→i(# int2bits(~ j)), j + 1 < 2 ^ n→i(# int2bits(~ j)) ⊦ 2 ^ n→i(# int2bits(~ j)) = 2 ^ (n→i(# uint2bits(2 ^ n→i(# int2bits(~ j)) + j)) - 1)

Rule argument

seq: ⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1)) subst: [j] → [~ j] rotate: F spec: int-pot inst: name: exin2pot

Additional information

Used terms: ~ j