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Theorem int2bits-falsein-01

⊦ i < ~1 → false ∈ int2bits(i).rest

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: int2bits-falsein-02, uint2bits-add-high,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 27
Proof steps: 50
Used lemmas: uint2bits-false, uint2bits-2pot-05, uint2bits-first-05, uint2bits-onein-01, int2bits-neg,
Used spec theorems:
- bitopsaux/succ-exinv
- bitopsaux/sgn-rec-01
- bitopsaux/sgn-base-03
- bitopsaux/sgn-append-06
- bitopsaux/sgn-append-05
- list/bitlista/rest-01
- bitopsaux/sgn-true
- list/bitlista/first-01
Used simplifier rules:
- list/bitlista/rest
- bitopsaux/sgn-empty-01
- bitopsaux/inv-in-02
- bitopsaux/inv-inv
- bitopsaux/inv-first-01
- list/bitlista/c-08
- bitopsaux/inv-first
- list/bitlista/in-06
- bitopsaux/inv-in-01
- list/bitlista/e-03
- list/bitlista/first-02
- list/bitlista/e
- bitopsaux/inv-empty
- list/bitlista/app-02-ant
- list/bitlista/len-02
- int-abs/negeq
- int-abs/numadd-01
- int-basic2/add-a
- int-basic2/add-c
- int-abs/negle-07
- int-basic2/add-zero
- int-abs/zero-gels-03
- list/bitlista/in-17
- list/bitlista/in-append
- list/bitlista/app-01
- list/bitlista/Last
- bitopsaux/succ-zero
- bitopsaux/inv-one-01
- list/bitlista/in-15
- list/bitlista/in-empty
- list/bitlista/app
- bitlista/somein
- list/bitlista/c-07
- bitopsaux/sgn-base-04
- bitopsaux/sgn-rec
- bitopsaux/invert-base
- list/bitlista/in-14
- list/bitlista/e-01
- bitopsaux/invert-zero
- list/bitlista/c
- list-data/bitlista/elim-list
- list/bitlista/Nil
- list/bitlista/in-13
- list/bitlista/a
- list/bitlista/neq
- int-abs/abs-08
- int-basic1/numlsf