He permitted spraying in M’chuzoh - שרא זילחא במחוזא
Summary:
There is no אשוויי גומות by stone floors when spraying
but there can be אשוויי גומות when washing the stone floors. Alternately there is no difference between spraying and washing, however by a stone floor it is a שבות חמור according to ר"א, which is אסור even במקדש.
And now that we are established according to Rabi Shimon it is permitted even initially - והאידנא דקיימא לן כרבי שמעון שרי אפילו לכתחלה
Summary:
The בה"ג permits sweeping with a broom while the ר"י prohibits it because it is moving מוקצה, making it a כלי שמלאכתו לאיסור, thus explaining why it cannot be moved מחמה לצל.
And there is a contradiction; Rabi Shimon says there is no difference between a perforated, etc. - ורמינהו רבי שמעון אומר אין בין נקוב כולי
Summary:
תוספות offers three explanations of אין בין נקוב לשאינו נקוב אלא וכולי according to the הו"א that it contradicts our משנה. A. that they are both considered either תלוש or מחובר depending on which is more strict; B. they are both considered מחובר; C. that regarding פאה מעשר וכלאים they are not regarded as שדך.