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Proof step 16 from proof bor-2pot-plus-01 (previous step)

j < 0, j ≤ 0 ⊦ bits2int(bitsinvert(bitsand(bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1)), true '))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsand(bits, bits0) = bits
Proof step 18:
bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1)) ≠ [] ∧ true ' = true ', j < 0, j ≤ 0 ⊦ bits2int(bitsinvert(bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1)))) = j

Rule argument

name: and-rec-01 rotate: F subst: [bits0, bits] → [true ', bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1))]

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ sgn(bits) = [] ↔ bits = [];% ⊦ ¬ bits +1 ≠ [] ↔ false; Used terms: true ', bitsinvert(sgn(bitsinvert(uint2bits(~ j)) +1))