The phrase "in case" cannot be used in these circumstances. Here are examples of when to use it: "In case I break my leg, please call my parents", "In case I cannot arrive in time, please leave without me.", "In case it starts to rain, make sure to bring the pets inside." You are trying to replace the conditional "if" with "in case", and it doesn't work. The phrase "in case" is setting up an alternate plan, also known as a contingency, if something happens. As for your other two phrases "provided" (not providing) and "as long as", examples: "Provided it doesn't rain, the party will go on as scheduled." "Provided we have enough money, we will be able to pay the bills." "Provided I remain healthy, I will be able to play soccer." You can replace "Provided" with "As long as" and the meaning is the same. You can use "if" as a substitute, but the sentences have to be rewritten as an "if...then" statement, i.e. "If it doesn't rain, then the party will go on as scheduled." Finally, the word is spelled "synonym".

The first phrase that sprung to mind was "in the event that..." Then I just decided to see if there were more synonyms for "if", and here they are: http://dictionary.reverso.net/english-synonyms/if Some of them won't fit neatly in place of "in case", because they suggest a stronger likelihood or knowledge of extra facts. Anyway, see what you like. ^^