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Theorem sgn-ex-01
⊦ true ∈ bits ∧ false ∈ bits → (∃ boolvar, n, boolvar0, bits0. bits = mklist(boolvar, n) + (boolvar0 + bits0) ∧ sgn(bits) = boolvar + boolvar0 + bits0 ∧ ¬(boolvar ↔ boolvar0) ∧ n ≠ 0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
intops
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 32
Used lemmas:
sgn-mklist-02
,
sgn-base-01
,
sgn-base-02
,
sgn-base-03
,
sgn-mklist-04
,
Used spec theorems:
bitlista
/
mklist-intro
Used simplifier rules:
list-data
/bitlista/
size-01
list
/bitlista/
len
list
/bitlista/
len-02
list
/bitlista/
c-06
list-data
/bitlista/
elim-list-c
bitlista
/
mklist-num-01
nat
/
elim-pred-c
list
/bitlista/
app-01
nat
/
pred-03
list
/bitlista/
app
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-in
bitlista
/
inmklist-01
list
/bitlista/
e-01
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
c-08
nat-basic2
/
oz
list
/bitlista/
c-04
list
/bitlista/
app-03
nat-basic2
/
c
nat-basic2
/
a
list-last
/bitlista/
mk-last
list-last
/bitlista/
mklist-one
list-last
/bitlista/
mk-plus
list
/bitlista/
in-13
list
/bitlista/
in-14
list
/bitlista/
a
list
/bitlista/
in-17
list
/bitlista/
in-append
list
/bitlista/
in-empty
list
/bitlista/
c