[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 36 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(uint2bits(i / 256)) = bits2bytes(uint2bits(i / 256)) ∧ i2b(bits2int(lastn(8, uint2bits(i / 256) + fillsgn(9, uint2bits(i % 256)).rest))) = bits2bytes(int2bits(i % 256)).last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 38:
8 = # fillsgn(9, uint2bits(i % 256)).rest, 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(uint2bits(i / 256)) = bits2bytes(uint2bits(i / 256)) ∧ i2b(bits2int(fillsgn(9, uint2bits(i % 256)).rest)) = bits2bytes(int2bits(i % 256)).last

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [fillsgn(9, uint2bits(i % 256)).rest, uint2bits(i / 256), 8] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used simplifier rules: ⊦ bits ≠ [] → # bits.rest = (# bits)-1;% ⊦ # bits ≤ n → # fillsgn(n, bits) = n; Used terms: fillsgn(9, uint2bits(i % 256)).rest, uint2bits(i / 256), 8