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Theorem cast-if

⊦ 0 < i → cast(i, j) = (0 ≤ j ∧ j % 2 ^ i ≤ 2 ^ (i - 1) - 1 ⊃ j % 2 ^ i ;(0 ≤ j ∧ 2 ^ (i - 1) - 1 < j % 2 ^ i ⊃ j % 2 ^ i - 2 ^ i ;(j < 0 ∧ j % 2 ^ i < ~(2 ^ (i - 1)) ⊃ j % 2 ^ i + 2 ^ i;(j < 0 ∧ ~(2 ^ (i - 1)) ≤ j % 2 ^ i ⊃ j % 2 ^ i;j)) ) )

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state: byte,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 16
Used lemmas: cast-size-fits-01, cast-mod-neg-high, cast-mod-neg-low, cast-mod-pos-high, cast-mod-pos-low,
Used spec theorems:
- Used simplifier rules: