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Proof step 10 from proof uint2bits-inj (previous step)

uint2bits(i / 2) + (i % 2 = 1)' = uint2bits(j), 0 < i, 0 ≤ j, 0 ≤ i, (i % 2 = 1) ∈ uint2bits(j), ∀ i0, j. i→n(i0) < i→n(i) → uint2bits(i0) = uint2bits(j) ∧ 0 ≤ i0 ∧ 0 ≤ j → i0 = j ⊦ i = j, i = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 12:
¬(0 < j ∧ j ≠ 1), uint2bits(i / 2) + (i % 2 = 1)' = uint2bits(j), 0 < i, 0 ≤ j, 0 ≤ i, (i % 2 = 1) ∈ uint2bits(j), ∀ i0, j. i→n(i0) < i→n(i) → uint2bits(i0) = uint2bits(j) ∧ 0 ≤ i0 ∧ 0 ≤ j → i0 = j ⊦ i = j, i = 1
Proof step 14:
0 < j ∧ j ≠ 1, uint2bits(i / 2) + (i % 2 = 1)' = uint2bits(j / 2) + (j % 2 = 1), 0 < i, 0 ≤ j, 0 ≤ i, (i % 2 = 1) ∈ uint2bits(j / 2) + (j % 2 = 1), ∀ i0, j. i→n(i0) < i→n(i) → uint2bits(i0) = uint2bits(j) ∧ 0 ≤ i0 ∧ 0 ≤ j → i0 = j ⊦ i = j, i = 1

Rule argument

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

Additional information

Used terms: j