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Proof step 38 from proof equal-minus-one (previous step)

~(1 / ~(i ^ ~ j)) = ~1, j < 0, i ^ ~ j < 0 ⊦ i = 0, i = ~1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
0 < j, j ≤ i ⊦ i / j = (i - j) / j + 1
Proof step 40:
~(1 / ~(i ^ ~ j)) = ~1, i ^ ~ j < 0, j < 0 ⊦ i = ~1, i = 0, j = 0, 0 < ~(i ^ ~ j) ∧ ~(i ^ ~ j) ≤ 1
Proof step 43:
~((1 - ~(i ^ ~ j)) / ~(i ^ ~ j) + 1) = ~1, i ^ ~ j < 0, j < 0, 0 < ~(i ^ ~ j), ~(i ^ ~ j) ≤ 1 ⊦ i = ~1, i = 0, j = 0

Rule argument

spec: int-div name: div-rec seq: 0 < j, j ≤ i ⊦ i / j = (i - j) / j + 1 subst: [j, i] → [~(i ^ ~ j), 1] flags: <all paths>

Additional information

Used terms: ~(i ^ ~ j), 1