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Theorem mult-emptymx-ind
⊦ n < m ∧ n1 ≤ # x → Σ(0 to n1, λ n0. ∅.toMatrix(m, # x)[n, n0] * x[n0]) = O
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
multzero
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 8
Used lemmas:
toMatrix-get
,
Used spec theorems:
natset
/
range-recend
matrixops
/
sum-rec
Used simplifier rules:
natset
/
range-empty
matrixops
/
sum-base
nat-basic
/
f
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
nat-basic
/
succ
nat-basic
/
add-base
nat
/
add-01
nat-basic
/
oz
nat-basic
/
zero
set-basic
/natset/
eq
natset
/
range-def
nat
/
lez
nat-basic
/
ref
ring
/
addcom
ring
/
addassoc
ring
/
addzero-r
ring
/
multassoc
ring
/
multzero-l
store
/sparsearray/
In-empty
nat
/
lels-03