[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 30 from proof bits2int-pos (previous step)

boolvar, 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0, 0 ≤ bits2int(fillsgn(8, int2bits(b2i(i2b(bits2int(boolvar ' + firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) ↔ ¬ boolvar

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i
Proof step 32:
¬(~128 ≤ bits2int(boolvar ' + firstn(# bits0 % 8, bits0)) ∧ bits2int(boolvar ' + firstn(# bits0 % 8, bits0)) ≤ 127), boolvar, 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0, 0 ≤ bits2int(fillsgn(8, int2bits(b2i(i2b(bits2int(boolvar ' + firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) ↔ ¬ boolvar
Proof step 40:
~128 ≤ bits2int(boolvar ' + firstn(# bits0 % 8, bits0)) ∧ bits2int(boolvar ' + firstn(# bits0 % 8, bits0)) ≤ 127, boolvar, 7 < # bits0, # bits0 % 8 ≤ 7, # bits0 % 8 < # bits0 ⊦ bits0 = [], (# bits0 + 1) % 8 = 0, 0 ≤ bits2int(fillsgn(8, int2bits(bits2int(boolvar ' + firstn(# bits0 % 8, bits0)))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) ↔ ¬ boolvar

Rule argument

seq: ~128 ≤ i, i ≤ 127 ⊦ b2i(i2b((* i))) = i subst: [i] → [bits2int(boolvar ' + firstn(# bits0 % 8, bits0))] rotate: F spec: byte inst: name: num-ibbi

Additional information

Used terms: bits2int(boolvar ' + firstn(# bits0 % 8, bits0))