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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 4:
0 < 2 ^ i ∧ 2 ^ i ≠ 1, 0 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 ≤ i0 → uint2bits(2 ^ i0) = false ' + true ' + mklist(false, i→n(i0)) ⊦ uint2bits(2 ^ i / 2) + (2 ^ i % 2 = 1) = false ' + true ' + mklist(false, i→n(i))

Rule argument

name: uint2bits-rec-01 rotate: F subst: [i] → [2 ^ i]

Additional information

Used simplifier rules: uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i ^ j = 1 ∧ 0 ≤ j → j = 0 ∨ abs(i) = 1; (forward)% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ bits = bits + bits0 ↔ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ i ≠ j → (i ≤ j ↔ i < j); Used terms: 2 ^ i