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Proof step 39 from proof bor-2pot-plus (previous step)

# int2bits(j0) = i→n(i) + 1, int2bits(j0) = false ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, i→n(i) ≤ # bits, false ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2uint(bits) + 2 ^ n→i(# bits) * j = j * 2 ^ i + j0, bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ bits2int(false ' + bits) = bits2uint(bits)
Proof step 41:
# int2bits(j0) = i→n(i) + 1, int2bits(j0) = false ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, i→n(i) ≤ # bits, false ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(false ' + bits) + 2 ^ n→i(# bits) * j = j * 2 ^ i + j0, bits = []

Rule argument

seq: ⊦ bits2int(false ' + bits) = bits2uint(bits) subst: [bits] → [bits] rotate: T spec: int2bits inst: name: bits2int-pos

Additional information

Used terms: bits