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Theorem sis-neg-high

⊦ i < 0 ∧ ~32768 ≤ i % 65536 → s2i(i2s(i)) = i % 65536

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: sis-ls-same, sis-ls-same-01, sis-neg-lower, sis-sub-2pot, ushort-pos-02,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 23
Proof steps: 38
Used lemmas: sis-06, num-i2s-neg, num-issi,
Used spec theorems:
Used simplifier rules:
- int-abs/forward-le-03
- int-abs/forward-le-01
- int-abs/absle
- int-abs/numadd-01
- bitopsaux/inv-one-01
- bitopsaux/sgn-two-01
- int-abs/numle-02
- list-data/bitlista/l
- nat-basic1/f
- nat/lels-01
- int-abs/numleledel-01
- int2bits/int2int-inj
- int2bits/int2bits-not-empty
- bitopsaux/fill-length
- int-basic1/numlslsdel-01
- list-last/bitlista/mk-len
- int2bits/bits2int-neg
- bitopsaux/inv-mklist
- bitopsaux/succ-mklist
- int2bits/bits2uint-2pot-02
- int-div/mod-two-pred-01
- int-div/div-mult-03
- int-mult/pred-rmerge
- int-abs/sub-sub
- int-basic1/ls-01
- int-mult/two-zero
- int-mult/neq-two
- int-mult/eq-one
- int-abs/sub-eq
- int-mult/succ-rmerge
- int-abs/Sub-def
- int-mult/eq-neg
- int-abs/lsone
- int-div/nummult-ls
- list/bitlista/len
- bitopsaux/sgn-base-01
- bitopsaux/sgn-rec
- bitopsaux/succ-zero
- bitopsaux/succ-rec
- list/bitlista/c
- bitopsaux/inv-false
- bitopsaux/invert-one
- bitopsaux/invert-zero
- list/bitlista/Last
- list/bitlista/Two
- int2bits/uint2bits-one
- int2bits/uint2bits-pos-num
- int2bits/int2bits-neg-num
- int-abs/sub-ls
- int-abs/minus-add
- int-abs/numle-03
- int-abs/negle-07
- int-abs/numlsledel-01
- int-abs/numls-02
- int-abs/neg-13
- int-abs/abs-08
- list/bitlista/a
- list-del/bitlista/lastn-mklist-01
- int-div/nummult-ls-01
- list/bitlista/len-02
- int2bits/int2bits-zero
- int-mult/associativity
- int-abs/zero-gels-01
- int-mult/zero-ls
- int-abs/lels-02
- int-abs/lels-04
- int-abs/zero-gels-03
- int-basic2/add-zero
- int-abs/anti
- int-mult/commutativity
- int-abs/forward-le-04
- int-basic1/numlsf
- int-basic2/add-c
- int-basic2/add-a
- int-abs/lels
- int-abs/lels-03
- int-div/div-elim-negpos
- int-basic1/lst
- int-abs/lels-01
- int-abs/forward-le-02