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Proof step 18 from proof int2int-lastn-posneg (previous step)

1 + # bits0 = # int2bits(i) - m, int2bits(i) = (false ' + bits0) + lastn(m, int2bits(i)), i = bits2uint(bits0) * 2 ^ n→i(m) + bits2uint(lastn(m, int2bits(i))), false ∈ int2bits(i), m ≤ # int2bits(i), lastn(m, int2bits(i)).first, 0 < i, 2 ^ n→i(m) ≤ bits2uint(lastn(m, int2bits(i))), 0 ≤ i ⊦ i % 2 ^ n→i(m) = bits2int(lastn(m, int2bits(i))) + 2 ^ n→i(m), m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ # bits ≤ n → ¬ 2 ^ n→i(n) ≤ bits2uint(bits)

Rule argument

name: bits2uint-nle-01 rotate: F subst: [bits, n] → [lastn(m, int2bits(i)), m]

Additional information

Used simplifier rules: ⊦ n ≤ # bits → # lastn(n, bits) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ n < n; Used terms: lastn(m, int2bits(i)), m