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Proof step 2 from proof cast-add-2pot-h (previous step)

j < 0, 0 < i, 0 < j + 2 ^ i ⊦ cast(i, j + 2 ^ i) = cast(i, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
j < 0, j % 2 ^ i < ~(2 ^ (i - 1)), 0 < i ⊦ cast(i, j) = j % 2 ^ i + 2 ^ i
Proof step 4:
¬(j < 0 ∧ j % 2 ^ i < ~(2 ^ (i - 1)) ∧ 0 < i), j < 0, 0 < i, 0 < j + 2 ^ i ⊦ cast(i, j + 2 ^ i) = cast(i, j)
Proof step 35:
j < 0 ∧ j % 2 ^ i < ~(2 ^ (i - 1)) ∧ 0 < i, j < 0, 0 < i, 0 < j + 2 ^ i ⊦ cast(i, j + 2 ^ i) = j % 2 ^ i + 2 ^ i

Rule argument

name: cast-mod-neg-low rotate: F subst: [j, i] → [j, i]

Additional information

Used terms: j, i