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Theorem int2bits-truein

⊦ true ∈ int2bits(j) ↔ j ≠ 0

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: bits2uint-zero-01, int2bits-add-high, int2bits-first-03, int2bits-first-04, int2bits-inv-first, int2bits-leading-sgn, int2bits-truein-01, int2bits-truetrue, int2bits-truetrue-01, int2int-rest-01, uint2bits-add-high-02,
Used by units in proved state: intops, bytes,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 8
Used lemmas: uint2bits-onein, uint2bits-onein-01, int2bits-neg, int2bits-pos, int2bits-zero,
Used spec theorems:
- bitopsaux/succ-exinv
- bitopsaux/sgn-in-01
Used simplifier rules:
- list/bitlista/e
- bitopsaux/inv-empty
- list/bitlista/app-02-ant
- list/bitlista/e-03
- list/bitlista/in-append
- bitopsaux/inv-in-02
- list/bitlista/in-06
- list/bitlista/in-13
- list/bitlista/a
- list/bitlista/neq
- int-abs/abs-08
- int-abs/lels-01
- list/bitlista/in-17
- int-abs/lels-02