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Proof step 26 from proof int2int-lastn-pospos (previous step)

0 ≤ bits2uint(bits0) * 2 ^ n→i(m) + bits2uint(lastn(m, int2bits(i))) ∧ 0 ≤ bits2uint(lastn(m, int2bits(i))) ∧ bits2uint(lastn(m, int2bits(i))) < 2 ^ n→i(m), 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), 0 < i, m ≤ # int2bits(i) ⊦ bits2int(lastn(m, int2bits(i))) = bits2uint(lastn(m, int2bits(i))), m = 0, lastn(m, int2bits(i)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)

Rule argument

name: bits2int-pos-02 rotate: F subst: [bits] → [lastn(m, int2bits(i))]

Additional information

Used simplifier rules: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ lastn(n, bits) = [] ↔ n = 0; Used terms: lastn(m, int2bits(i))