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Proof step 62 from proof uint2bits-mod2pot (previous step)

i1 % 2 ^ i0 = 0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), 0 < i1, 2 ^ i0 < i1, 0 ≤ i1, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 0) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + false ')

User applied rule insert elim lemma

And obtained the following new goals

Proof step 63:
i1 = i2 * 2 ^ i0 + j ∧ 0 ≤ j ∧ j < 2 ^ i0 ∧ 0 < 2 ^ i0, j = 0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), 0 < i1, 2 ^ i0 < i1, 0 ≤ i1, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 0) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + false ')

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [i1, 2 ^ i0, i2, j] rotate: T spec: int-div inst: name: div-elim-pos

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j → ¬ j < i;%⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j); (elim) Used terms: i1, 2 ^ i0, i2, j