correctokspmx(spmx, r, # x) ⊦ ⟪MULT#(spmx, r, x; ; y)⟫ (y = spmx.toMatrix(r, # x) * x)multzerookspmx-defmain-lemmatoMatrix-rownotoMatrix-colnoaddzeroMULT
830correct-proofcorrect-proof-info
The proof is valid.
../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/multmxvec-size/longlemmainfo.xmlmultmxvec-size../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/Extension/longlemmainfo.xmlExtension../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/addvec-com/longlemmainfo.xmladdvec-com../../../../../../lib/basic/specs/array/export/unit.xmlarraymatrixops../../../../../../lib/basic/specs/array/export/Size-mkarray/longlemmainfo.xmlSize-mkarray../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/sub-ref/longlemmainfo.xmlsub-ref../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/f/longlemmainfo.xmlf../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/c/longlemmainfo.xmlc../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/a/longlemmainfo.xmla../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/ref/longlemmainfo.xmlref../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/s-04/longlemmainfo.xmls-04../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/ls-01/longlemmainfo.xmlls-01../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/empty/longlemmainfo.xmlempty../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/one-01/longlemmainfo.xmlone-01../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/le-def/longlemmainfo.xmlle-def../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/pred-03/longlemmainfo.xmlpred-03../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/size/longlemmainfo.xmlsize../../../../../../lib/basic/specs/array/export/unit.xmlarraymatrixops../../../../../../lib/basic/specs/array/export/Size-put/longlemmainfo.xmlSize-put../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/subset-delete-02/longlemmainfo.xmlsubset-delete-02../../../../../../lib/basic/specs/ring/export/unit.xmlring../../../../../../lib/basic/specs/ring/export/multassoc/longlemmainfo.xmlmultassoc../../../../../../lib/basic/specs/ring/export/unit.xmlring../../../../../../lib/basic/specs/ring/export/addassoc/longlemmainfo.xmladdassoc../../../../../../lib/basic/specs/ring/export/unit.xmlring../../../../../../lib/basic/specs/ring/export/addcom/longlemmainfo.xmladdcom../../../../specs/natpair/export/unit.xmlnatpair../../../../specs/natpair/export/elim/longlemmainfo.xmlelim../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/lels/longlemmainfo.xmllels../../../../specs/natpair/export/unit.xmlnatpair../../../../specs/natpair/export/sel-01/longlemmainfo.xmlsel-01../../../../specs/natpair/export/unit.xmlnatpair../../../../specs/natpair/export/sel-02/longlemmainfo.xmlsel-02../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/le-ls-simp/longlemmainfo.xmlle-ls-simp../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/superset-elem-in-01/longlemmainfo.xmlsuperset-elem-in-01../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/notmemlookup/longlemmainfo.xmlnotmemlookup../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/In-empty/longlemmainfo.xmlIn-empty../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/subset-empty/longlemmainfo.xmlsubset-empty