[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 31 from proof int2bytes-rec-pos (previous step)

uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, # uint2bits(i % 256) ≤ 9, 255 < i, 0 < i, 0 ≤ i ⊦ fillsgn(9, uint2bits(i % 256)) = [], bits2bytes(firstn(# uint2bits(i / 256), uint2bits(i))) + i2b(bits2int(lastn(8, uint2bits(i)))) ' = bits2bytes(uint2bits(i / 256)) + bits2bytes(int2bits(i % 256)).last '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ bytes + by ' = bytes0 + by0 ' ↔ bytes = bytes0 ∧ by = by0
Proof step 33:
uint2bits(i) = uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest, # uint2bits(i % 256) ≤ 9, 255 < i, 0 < i, 0 ≤ i ⊦ fillsgn(9, uint2bits(i % 256)) = [], bits2bytes(firstn(# uint2bits(i / 256), uint2bits(i))) = bits2bytes(uint2bits(i / 256)) ∧ i2b(bits2int(lastn(8, uint2bits(i)))) = bits2bytes(int2bits(i % 256)).last

Rule argument

seq: ⊦ bytes + by ' = bytes0 + by0 ' ↔ bytes = bytes0 ∧ by = by0 subst: [by0, bytes0, by, bytes] → [bits2bytes(int2bits(i % 256)).last, bits2bytes(uint2bits(i / 256)), i2b(bits2int(lastn(8, uint2bits(i)))), bits2bytes(firstn(# uint2bits(i / 256), uint2bits(i)))] rotate: F spec: list inst: bytelist name: app-06

Additional information

Used terms: bits2bytes(int2bits(i % 256)).last, bits2bytes(uint2bits(i / 256)), i2b(bits2int(lastn(8, uint2bits(i)))), bits2bytes(firstn(# uint2bits(i / 256), uint2bits(i)))