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Theorem intshiftleft-is-mult-01

⊦ i i<< j = i * 2 ^ band(j, 31)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 19
Proof steps: 36
Used lemmas: band-011x-pos-02, band-011x-neg-02, intshiftleft,
Used spec theorems:
Used simplifier rules:
- int-abs/lels-03
- int-abs/forward-le-05
- int-abs/lels-02
- int-mult/eq-nonzero
- int-mult/neq-not-zero
- int2bits/int2uint-pos-01
- int2bits/bits2uint-zeros-04
- int-basic1/numlsf
- int-abs/numls-03
- int-pot/zero-02
- int-mult/eq-same
- int-basic2/add-zero
- int-mult/Mult-zero
- int-pot/two-minus
- int-abs/abs-08
- int-abs/numadd-01
- int-abs/absle
- int-mult/succ-rmerge
- int-abs/lels-04
- int-abs/lels-01
- int-abs/zero-gels-01
- int-abs/forward-lsle
- int-abs/forward-le-01
- list/bitlista/in-17
- list/bitlista/in-append
- list/bitlista/c-07
- list/bitlista/Last
- list/bitlista/Two
- int2bits/uint2bits-one
- int2bits/uint2bits-pos-num
- int-abs/lels
- int-basic2/add-c
- int-basic2/add-a
- int-abs/Sub-def
- bitlista/inmklist-01
- list-last/bitlista/mk-empty
- int-abs/sub-eq
- bitopsaux/inv-mklist
- int-abs/neg-02
- int-mult/minus-left
- intnat/ini2-abs
- int-abs/subsub
- int2bits/int2uint-inv-01
- int2bits/int2bits-first-01
- int-abs/forward-le-02
- list-last/bitlista/mk-zero
- list/bitlista/app
- list/bitlista/a
- int2bits/int2int-inj
- int-mult/one
- int-mult/associativity
- int-mult/commutativity
- int2bits/int2bits-first-02
- int2bits/int2bits-not-empty
- list-data/bitlista/l
- intnat/abs-zero
- list-last/bitlista/mk-len