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Proof step 38 from proof intshiftrsign-rec-pos (previous step)

0 ≤ i, i0 < 31, 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i ⊦ bits2int ( sublist(0, # int2bits(i / 2), (false ' + mklist(false, i→n(i0))) + int2bits(i / 2) + (i % 2 = 1)') + ((false ' + mklist(false, i→n(i0))) + int2bits(i / 2) + (i % 2 = 1)')[# int2bits(i / 2)] ') = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ (bits + bits0) + bits1 = bits + bits0 + bits1
Proof step 40:
0 ≤ i, i0 < 31, 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i ⊦ bits2int ( sublist(0, # int2bits(i / 2), ((false ' + mklist(false, i→n(i0))) + int2bits(i / 2)) + (i % 2 = 1)') + (((false ' + mklist(false, i→n(i0))) + int2bits(i / 2)) + (i % 2 = 1)')[# int2bits(i / 2)] ') = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2)))

Rule argument

seq: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1 subst: [bits1, bits0, bits] → [(i % 2 = 1)', int2bits(i / 2), false ' + mklist(false, i→n(i0))] rotate: T spec: list inst: bitlista name: a

Additional information

Used terms: (i % 2 = 1)', int2bits(i / 2), false ' + mklist(false, i→n(i0))