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Theorem band-011x-is-unsigned-01

⊦ ¬ false ∈ int2bits(i0).rest ∧ abs(j) ≤ 2 ^ n→i(# int2bits(i0) - 2) ∧ 0 < i0 → band(j, i0) = bits2uint(fillsgn(# int2bits(i0) - 1, int2bits(j)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: band-011x-is-unsigned-03, band-011x-is-unsigned-fix,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 6
Used lemmas: band-011x-is-unsigned,
Used spec theorems:
- int2bits/int2bits-falsein-02
- intnat/num-n2i-ls-06
Used simplifier rules:
- intnat/num-i2n-le-02
- int-abs/zero-gels-04
- nat/le-num-04
- nat/ls-02
- nat/le-num-02
- nat/le-add
- nat-basic1/z
- intnat/num-n2i-ls-02
- int-abs/forward-le
- int-basic2/add-c
- int-basic2/add-a
- int-abs/succ-02
- int-abs/sub-ls
- int-pot/ls-pos-2pot-01
- int-abs/sub-le-01
- int-abs/leone
- int-abs/forward-lsle
- int-abs/lels-03
- int-abs/lels
- int-abs/sub-ls-01
- int-pot/pot2-pos-01
- int-basic1/ls-01
- nat-basic2/c
- nat-basic2/a
- nat-basic2/z
- nat/add-01
- list/bitlista/a
- list-last/bitlista/mk-len
- list/bitlista/len-02
- list/bitlista/len
- int2bits/int2bits-2pot-02
- int-abs/lels-01
- int-pot/two-minus
- int-abs/forward-le-05