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Proof step 2 from proof cast-mod-pos-high (previous step)

2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j ⊦ j % 2 ^ i = cast(i, j) + 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
0 < i, ~(2 ^ (i - 1)) ≤ j, j < 2 ^ (i - 1) ⊦ cast(i, j) = j
Proof step 4:
¬(0 < i ∧ ~(2 ^ (i - 1)) ≤ j ∧ j < 2 ^ (i - 1)), 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j ⊦ j % 2 ^ i = cast(i, j) + 2 ^ i
Proof step 68:
0 < i ∧ ~(2 ^ (i - 1)) ≤ j ∧ j < 2 ^ (i - 1), 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j ⊦ j % 2 ^ i = j + 2 ^ i

Rule argument

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

Additional information

Used terms: j, i