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Proof step 51 from proof bor-2pot-plus-01 (previous step)

# int2bits(j0) = i→n(i) + 1, 0 ≤ 2 ^ i, 0 < 2 ^ i, j + 1 < j0, 0 < j0, j < 0, j + 1 < i, 0 ≤ j0, j < i, j < j0, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 < i, i→n(i) ≤ # int2bits(j0).rest, 1 < 2 ^ i, 2 + j < 2 ^ i ⊦ int2bits(j0).rest = [], i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], (j + 1) * 2 ^ n→i(# int2bits(j0).rest) = 2 ^ (n→i(# uint2bits(j0)) - 1) + j * 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ bits ≠ [] → # bits.rest = (# bits)-1
Proof step 53:
int2bits(j0) ≠ [], # int2bits(j0) = i→n(i) + 1, 0 ≤ 2 ^ i, 0 < 2 ^ i, j + 1 < j0, 0 < j0, j < 0, j + 1 < i, 0 ≤ j0, j < i, j < j0, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 < i, i→n(i) ≤ (# int2bits(j0))-1, 1 < 2 ^ i, 2 + j < 2 ^ i ⊦ int2bits(j0).rest = [], i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], (j + 1) * 2 ^ n→i((# int2bits(j0))-1) = 2 ^ (n→i(# uint2bits(j0)) - 1) + j * 2 ^ i

Rule argument

seq: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [int2bits(j0)] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j0)