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Proof step 16 from proof bytes2int-mone (previous step)
| b2i(by) < 0 ⊦ bits2int(sgn(true ' + byte2bits(by) + bytes2bits(bytes))) = bits2int(byte2bits(by) + bytes2bits(bytes)) |
User applied rule insert rewrite lemma
And obtained the following new goals
- Proof step 17:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
- Proof step 18:
¬(byte2bits(by) + bytes2bits(bytes) ≠ [] ∧ ((byte2bits(by) + bytes2bits(bytes)).first ↔ true)), b2i(by) < 0
⊦ bits2int(sgn(true ' + byte2bits(by) + bytes2bits(bytes))) = bits2int(byte2bits(by) + bytes2bits(bytes))
Rule argument
seq: bits ≠ [], bits.first ↔ boolvar
⊦ sgn(boolvar ' + bits) = sgn(bits)
subst: [bits, boolvar] → [byte2bits(by) + bytes2bits(bytes), true]
rotate: F
spec: bitopsaux
inst:
name: sgn-rec-01Additional information
Used simplifier rules:
⊦ bits2int(sgn(bits)) = bits2int(bits);%⊦ bits ≠ [] ∧ bits0 ≠ []
→ (bits2int(bits) = bits2int(bits0) ↔ sgn(bits) = sgn(bits0));
Used terms: byte2bits(by) + bytes2bits(bytes), true