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Theorem to-append-add
⊦ ¬ # σ < ⌜n⌝ ∧ ¬ # σ0 < ⌜n1⌝ → ⌜σ to n⌝ + σ0 to n1 + n = (σ to n) + (σ0 to n1)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
toinfto-append-add
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas:
to-zero
,
to-to-eq
,
size-to
,
size-to-02
,
append-assoc
,
to-fin
,
append-le-to
,
append-gr-to
,
Used spec theorems:
Used simplifier rules:
stream-basic
/
sel-rqui-dotl
nat
/
eq-01
nat-basic
/
a
nat-basic
/
c
list
/
len-01
list
/
a
nat-inf
/
add-fin
nat-inf
/
ls-natinf-to-nat-1-2
nat
/
lels
nat
/
le-add
nat-inf
/
add-assoc
nat-inf
/
add-comm
nat-basic
/
add-base
list
/
app