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) * xtoMatrix-colnotoMatrix-rownotoMatrix-add915main-lemma-proofmain-lemma-proof-infolssThe proof is valid.lsscorrect../../../../specs/VF3conc/export/unit.xmlVF3conc../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/exin/longlemmainfo.xmlexin../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/distrmxmxvec/longlemmainfo.xmldistrmxmxvec../../../../../../lib/basic/specs/array/export/unit.xmlarraymatrixops../../../../../../lib/basic/specs/array/export/Extension/longlemmainfo.xmlExtension../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/addmvec-get/longlemmainfo.xmladdmvec-get../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/multmxvec-size/longlemmainfo.xmlmultmxvec-size../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/singletonmxvec-get/longlemmainfo.xmlsingletonmxvec-get../../../../../../lib/basic/specs/array/export/unit.xmlarraymatrixops../../../../../../lib/basic/specs/array/export/Put-other/longlemmainfo.xmlPut-other../../../../../../lib/basic/specs/nat-basic/export/unit.xmlnat-basic../../../../../../lib/basic/specs/nat-basic/export/f/longlemmainfo.xmlf../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/notin-del-notin/longlemmainfo.xmlnotin-del-notin../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/Del-rec-same/longlemmainfo.xmlDel-rec-same../../../../../../lib/basic/specs/store/export/unit.xmlstoresparsearray../../../../../../lib/basic/specs/store/export/k-At-same/longlemmainfo.xmlk-At-same../../../../../../lib/basic/specs/matrix/export/unit.xmlmatrix../../../../../../lib/basic/specs/matrix/export/rowno-put/longlemmainfo.xmlrowno-put../../../../../../lib/basic/specs/matrix/export/unit.xmlmatrix../../../../../../lib/basic/specs/matrix/export/rowno-mkmatrix/longlemmainfo.xmlrowno-mkmatrix../../../../../../lib/basic/specs/matrix/export/unit.xmlmatrix../../../../../../lib/basic/specs/matrix/export/colno-put/longlemmainfo.xmlcolno-put../../../../../../lib/basic/specs/matrix/export/unit.xmlmatrix../../../../../../lib/basic/specs/matrix/export/colno-mkmatrix/longlemmainfo.xmlcolno-mkmatrix../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/addmvec-get/longlemmainfo.xmladdmvec-get../../../../../../lib/basic/specs/array/export/unit.xmlarraymatrixops../../../../../../lib/basic/specs/array/export/Size-put/longlemmainfo.xmlSize-put../../../../../../lib/basic/specs/matrixops/export/unit.xmlmatrixops../../../../../../lib/basic/specs/matrixops/export/addvec-size/longlemmainfo.xmladdvec-size../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/fle-01/longlemmainfo.xmlfle-01../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/lels/longlemmainfo.xmllels../../../../../../lib/basic/specs/nat/export/unit.xmlnat../../../../../../lib/basic/specs/nat/export/ls-le-simp/longlemmainfo.xmlls-le-simp../../../../../../lib/basic/specs/ring/export/unit.xmlring../../../../../../lib/basic/specs/ring/export/addzero-r/longlemmainfo.xmladdzero-r../../../../../../lib/basic/specs/ring/export/unit.xmlring../../../../../../lib/basic/specs/ring/export/addcom/longlemmainfo.xmladdcom../../../../../../lib/basic/specs/ring/export/unit.xmlring../../../../../../lib/basic/specs/ring/export/addassoc/longlemmainfo.xmladdassoc../../../../../../lib/basic/specs/array/export/unit.xmlarraymatrixops../../../../../../lib/basic/specs/array/export/Put-same/longlemmainfo.xmlPut-same