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Proof step 37 from proof equal-minus-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
0 < j, j ≤ i ⊦ i / j = (i - j) / j + 1
Proof step 39:
¬(0 < ~(i ^ ~ j) ∧ ~(i ^ ~ j) ≤ 1), i ^ ~ j < 0, ~(1 / ~(i ^ ~ j)) = ~1, j < 0, i ^ ~ j < 0 ⊦ j = 0, i = ~1, i = 0
Proof step 42:
0 < ~(i ^ ~ j) ∧ ~(i ^ ~ j) ≤ 1, i ^ ~ j < 0, ~((1 - ~(i ^ ~ j)) / ~(i ^ ~ j) + 1) = ~1, j < 0, i ^ ~ j < 0 ⊦ j = 0, i = ~1, i = 0

Rule argument

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

Additional information

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