[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 79 from proof byte-law-righthift-not (previous step)

32 = n + # int2bits(128), i2b(bits2uint(firstn(31, mklist(false, n) + int2bits(128)))) = i2b(bits2uint(firstn(31, fillsgn(32, int2bits(~128))))), # int2bits(128) ≤ 32, # int2bits(~128) ≤ 32 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 80:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 81:
# int2bits(~128) ≤ 32 ∧ int2bits(~128) ≠ [], 32 = n + # int2bits(128), i2b(bits2uint(firstn(31, mklist(false, n) + int2bits(128)))) = i2b(bits2uint(firstn(31, mklist(int2bits(~128).first, 32 - # int2bits(~128)) + int2bits(~128)))), # int2bits(128) ≤ 32, # int2bits(~128) ≤ 32 ⊦

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [int2bits(~128), 32] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ int2bits(j) ≠ []; Used terms: int2bits(~128), 32