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Proof step 24 from proof band-011x-neg-03 (previous step)

0 ≤ i, 0 < j, i + 1 < j ⊦ (1 - j) % (i + 1) = ((i + 1) + (1 - j)) % (i + 1), false ∈ int2bits(i).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ 0 < i ∧ j < 0 ∧ i ≤ abs(j) → (i + j) % i = j % i
Proof step 26:
¬(0 < i + 1 ∧ 1 - j < 0 ∧ i + 1 ≤ abs(1 - j)), 0 ≤ i, 0 < j, i + 1 < j ⊦ (1 - j) % (i + 1) = ((i + 1) + (1 - j)) % (i + 1), false ∈ int2bits(i).rest

Rule argument

seq: ⊦ 0 < i ∧ j < 0 ∧ i ≤ abs(j) → (i + j) % i = j % i subst: [j, i] → [1 - j, i + 1] rotate: F spec: int-div inst: name: mod-add-01

Additional information

Used simplifier rules: ⊦ i + j = j + i; Used terms: 1 - j, i + 1