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Proof step 15 from proof uint2bits-2pot (previous step)

uint2bits(2 ^ i1) = false ' + true ' + mklist(false, i→n(i1)), 0 < 2 ^ (i1 + 1), ~1 ≤ i1, 0 < i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 0 ≤ i0 → uint2bits(2 ^ i0) = false ' + true ' + mklist(false, i→n(i0)) ⊦ 2 ^ (i1 + 1) = 1, uint2bits(2 ^ i1) + false ' = false ' + true ' + false ' + mklist(false, i→n(i1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
uint2bits(2 ^ i1) = false ' + true ' + mklist(false, i→n(i1)), false ∈ uint2bits(2 ^ i1), 0 < i1, ~1 ≤ i1, 0 < 2 ^ (i1 + 1), ∀ i0. i→n(i0) < i→n(i1 + 1) → 0 ≤ i0 → uint2bits(2 ^ i0) = false ' + true ' + mklist(false, i→n(i0)) ⊦ uint2bits(2 ^ i1) + false ' = false ' + true ' + false ' + mklist(false, i→n(i1)), 2 ^ (i1 + 1) = 1

Rule argument

Additional information

Used simplifier rules: ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits;% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)