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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: simp, localsimp,
Comment:
Used by:
toinftoinf-append-add
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas:
get-append-notls
,
get-append-ls
,
get-to
,
append-assoc
,
size-to
,
size-append
,
extensionality
,
Used spec theorems:
Used simplifier rules:
nat-basic1
/
f
nat-inf
/
ls-natinf-to-nat-1-2
nat-inf
/
eq-natinf-to-nat-2-2
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
add-ls-cancel-01
nat-basic2
/
a
nat-inf
/
add-fin
nat-inf
/
less-fin
nat
/
lels
nat
/
ls-le-simp
nat-inf-basic
/
sel
nat
/
lels-01
nat
/
ls-01
nat-basic2
/
c