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Proof step 4 from proof cast-law-add-one (previous step)

0 < i ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0), ¬ j < 0 ∧ ¬ j0 < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ j ∧ 0 < i → cast(i, j + j0) = cast(i, cast(i, j) + j0)
Proof step 6:
¬(0 ≤ j ∧ 0 < i), 0 < i ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0), ¬ j < 0 ∧ ¬ j0 < 0

Rule argument

name: cast-law-add-pos-01 rotate: F subst: [j0, j, i] → [j0, j, i]

Additional information

Used simplifier rules: ⊦ i + j = j + i; Used terms: j0, j, i