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Proof step 13 from proof int2int-lastn-pospos (previous step)

bits2int(int2bits(i)) = bits2int(bits + lastn(m, int2bits(i))), # bits = # int2bits(i) - m, int2bits(i) = bits + lastn(m, int2bits(i)), 0 < i, m ≤ # int2bits(i) ⊦ bits = [], bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), m = 0, lastn(m, int2bits(i)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 15:
¬(# lastn(m, int2bits(i)) ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first), bits2int(int2bits(i)) = bits2int(bits + lastn(m, int2bits(i))), # bits = # int2bits(i) - m, int2bits(i) = bits + lastn(m, int2bits(i)), 0 < i, m ≤ # int2bits(i) ⊦ bits = [], bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), m = 0, lastn(m, int2bits(i)).first
Proof step 17:
# lastn(m, int2bits(i)) ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first, bits2int(int2bits(i)) = bits2uint(bits) * 2 ^ n→i(# lastn(m, int2bits(i))) + bits2uint(lastn(m, int2bits(i))), # bits = # int2bits(i) - m, int2bits(i) = bits + lastn(m, int2bits(i)), 0 < i, m ≤ # int2bits(i) ⊦ bits = [], bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), m = 0, lastn(m, int2bits(i)).first

Rule argument

name: bits2int-split rotate: F subst: [bits0, bits] → [lastn(m, int2bits(i)), bits]

Additional information

Used terms: lastn(m, int2bits(i)), bits