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Proof step 48 from proof bor-2pot-plus-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ 0 < i → bits2uint(bitsinvert(int2bits(i).rest)) = 2 ^ (n→i(# uint2bits(i)) - 1) - i + 1
Proof step 50:
0 < j0, # int2bits(j0) = i→n(i) + 1, j < 0, j + 1 < i, 0 ≤ j0, 0 < 2 ^ i, j < i, j < j0, j + 1 < 2 ^ i, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1, j < 2 ^ i, j0 < 2 ^ i, 0 < i, i→n(i) ≤ # int2bits(j0).rest ⊦ i = 0, bitsinvert(int2bits(j)) + mklist(true, i→n(i)) = [], (j + 1) * 2 ^ n→i(# int2bits(j0).rest) = (j * 2 ^ i + j0) + (2 ^ (n→i(# uint2bits(j0)) - 1) - j0 + 1) + 1, int2bits(j0).rest = []

Rule argument

seq: ⊦ 0 < i → bits2uint(bitsinvert(int2bits(i).rest)) = 2 ^ (n→i(# uint2bits(i)) - 1) - i + 1 subst: [i] → [j0] rotate: F spec: int2bits inst: name: int2unit-inv-rest

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward)% ⊦ int2bits(0) = false ';% ⊦ # boolvar ' = 0 +1;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: j0