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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ bits.first → bits2int(bits + bits0) = ~(2 ^ n→i(# bits0) * bits2uint(bitsinvert(bits))) - bits2uint(bitsinvert(bits0)) + 1
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)), m ≤ # int2bits(i), lastn(m, int2bits(i)).first, i < 0 ⊦ bits = [], i + 2 ^ n→i(m) = 0, bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), m = 0
Proof step 17:
# lastn(m, int2bits(i)) ≠ 0 ∧ # bits ≠ 0 ∧ bits.first, bits2int(int2bits(i)) = ~(2 ^ n→i(# lastn(m, int2bits(i))) * bits2uint(bitsinvert(bits))) - bits2uint(bitsinvert(lastn(m, int2bits(i)))) + 1, # bits = # int2bits(i) - m, int2bits(i) = bits + lastn(m, int2bits(i)), m ≤ # int2bits(i), lastn(m, int2bits(i)).first, i < 0 ⊦ bits = [], i + 2 ^ n→i(m) = 0, bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m), m = 0

Rule argument

name: bits2int-split-01 rotate: F subst: [bits0, bits] → [lastn(m, int2bits(i)), bits]

Additional information

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