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Proof step 8 from proof bits2int-nls (previous step)

bits2int(bits) < 0, 2 ^ n→i(# bits) + bits2int(bits) < 0, 2 + # bits ≤ # int2bits(~ bits2int(bits)) ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 10:
0 ≤ ~ bits2int(bits), bits2int(bits) < 0, 2 ^ n→i(# bits) + bits2int(bits) < 0, 2 + # bits ≤ # uint2bits(~ bits2int(bits)) ⊦ bits = []

Rule argument

name: int2bits-pos rotate: F subst: [i] → [~ bits2int(bits)]

Additional information

Used simplifier rules: ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: ~ bits2int(bits)