[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem toMatrix-add
⊦ r < m ∧ c < n ∧ ¬ r × c ∈ spmx → spmx[r × c, a].toMatrix(m, n) = spmx.toMatrix(m, n) + mkmatrix(m, n, O)[r, c, a]
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
main-lemma
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 13
Used lemmas:
toMatrix-get
,
toMatrix-colno
,
toMatrix-rowno
,
Used spec theorems:
matrix
/
extension
matrixops
/
addmx-get
matrix
/
cngetput-c
matrix
/
cngetput-num-r
Used simplifier rules:
nat-basic
/
f
matrixops
/
addmx-colno
matrixops
/
addmx-rowno
ring
/
addzero-r
ring
/
addassoc
ring
/
addcom
store
/sparsearray/
In-insert
natpair
/
inj
nat-basic
/
lf-02
store
/sparsearray/
k-At-same
matrix
/
rowno-mkmatrix
matrix
/
colno-mkmatrix
matrix
/
cgetput
store
/sparsearray/
At-in-out
matrix
/
get-mkmatrix
store
/sparsearray/
notmemlookup
matrix
/
put-otherrow