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Theorem correct
okspmx(spmx, r, # x) ⊦ ⟪MULT#(spmx, r, x; ; y)⟫ (y = spmx.toMatrix(r, # x) * x)
Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 30
Used lemmas:
multzero
,
okspmx-def
,
main-lemma
,
toMatrix-rowno
,
toMatrix-colno
,
addzero
,
MULT
,
Used spec theorems:
matrixops
/
multmxvec-size
store
/sparsearray/
Extension
matrixops
/
addvec-com
Used simplifier rules:
array
/matrixops/
Size-mkarray
store
/sparsearray/
sub-ref
nat-basic
/
f
nat-basic
/
c
nat-basic
/
a
nat-basic
/
ref
nat-basic
/
s-04
nat
/
ls-01
store
/sparsearray/
empty
nat-basic
/
one-01
nat
/
le-def
nat
/
pred-03
store
/sparsearray/
size
array
/matrixops/
Size-put
store
/sparsearray/
subset-delete-02
ring
/
multassoc
ring
/
addassoc
ring
/
addcom
natpair
/
elim
nat
/
lels
natpair
/
sel-01
natpair
/
sel-02
nat
/
le-ls-simp
store
/sparsearray/
superset-elem-in-01
store
/sparsearray/
notmemlookup
store
/sparsearray/
In-empty
store
/sparsearray/
subset-empty