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Proof step 2 from proof int2int-lastn-posneg (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
n ≤ # bits ⊦ ∃ bits0. bits = bits0 + lastn(n, bits) ∧ # bits0 = # bits - n
Proof step 4:
∃ bits0. int2bits(i) = bits0 + lastn(m, int2bits(i)) ∧ # bits0 = # int2bits(i) - m, 0 < i, lastn(m, int2bits(i)).first, m ≤ # int2bits(i) ⊦ m = 0, i % 2 ^ n→i(m) = bits2int(lastn(m, int2bits(i))) + 2 ^ n→i(m)

Rule argument

seq: n ≤ # bits ⊦ ∃ bits0. bits = bits0 + lastn(n, bits) ∧ # bits0 = # bits - n subst: [n, bits] → [m, int2bits(i)] rotate: F spec: list-del inst: bitlista name: lastN-ex

Additional information

Used terms: m, int2bits(i)