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Theorem main-lemma
⊦ r × c ∈ spmx ∧ c < # x ∧ r < # y → y[r, y[r] + spmx[r × c] * x[c]] + (spmx -- (r × c)).toMatrix(# y, # x) * x = y + spmx.toMatrix(# y, # x) * x
Type: A user defined theorem
Validity: The proof is valid.
Features: ls, s,
Comment:
Used by:
correct
,
Used by units in proved state:
VF3conc
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 15
Used lemmas:
toMatrix-colno
,
toMatrix-rowno
,
toMatrix-add
,
Used spec theorems:
store
/sparsearray/
exin
matrixops
/
distrmxmxvec
array
/matrixops/
Extension
matrixops
/
addmvec-get
matrixops
/
multmxvec-size
matrixops
/
singletonmxvec-get
array
/matrixops/
Put-other
Used simplifier rules:
nat-basic
/
f
store
/sparsearray/
notin-del-notin
store
/sparsearray/
Del-rec-same
store
/sparsearray/
k-At-same
matrix
/
rowno-put
matrix
/
rowno-mkmatrix
matrix
/
colno-put
matrix
/
colno-mkmatrix
matrixops
/
addmvec-get
array
/matrixops/
Size-put
matrixops
/
addvec-size
nat
/
fle-01
nat
/
lels
nat
/
ls-le-simp
ring
/
addzero-r
ring
/
addcom
ring
/
addassoc
array
/matrixops/
Put-same