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Theorem band-011x-eq

⊦ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(i - j, i) + band(j, i) = i

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: band-011x-eq-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 11
Proof steps: 22
Used lemmas: band-011x-neg-02, band-commutativity, band-associativity, band-011x-neg-01, band-011x-pos-02,
Used spec theorems:
Used simplifier rules:
- int-pot/eq-two
- int-basic2/ls
- int-abs/zero-gels-04
- int-abs/succ-01
- int-basic1/ls-01
- int-abs/succ-02
- int-abs/sub-ls
- int-abs/lels-03
- int-abs/forward-le-05
- int-abs/neg-03
- int-abs/numls-03
- int-abs/lels
- int-abs/mone-08
- int-pot/two-zero
- int-div/mod-zero-04
- int-abs/sub-zero-01
- int-div/mod-same
- int-basic2/eq
- int-abs/absle
- int-pot/pot2-pos
- int-abs/leone
- int-abs/Sub-def
- int-abs/sub-sub
- intnat/ini2-abs
- 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-pot/two-minus
- int-abs/zero-gels-03
- int-abs/sub-le-01
- int-basic2/add-zero
- int-abs/zero-gels
- int-abs/zero-gels-01
- int-abs/forward-le-02
- int-abs/forward-lsle
- int-abs/sub-eq
- int-basic2/add-c
- int-basic2/add-a
- int-abs/sub-add-01
- int-abs/lels-04
- int-abs/lels-01
- int-abs/forward-le-01