Managing assumptions

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About conjunctions

A term made by joining other terms with & is called a conjunction, and we consider all of those terms to be part of the conjunction. For example A & B & C & D is commonly viewed as a conjunction of four terms rather than three separate conjunctions.

If we make all of the parentheses explicit, the conjunction

looks like this:

In this form we can see that there are really three conjunctions there, one for each occurrence of the and operator.

If we rearrange the terms in these larger conjunctions, the same input values still give the same result as before, so the conjunction is equivalent (equal) to the original. For example

which is a tautology. Also, if a conjunction has multiple occurrences of the same term, the duplicates can be removed and the result is still equivalent to the original.