Subsequent, Consequent... Presequent?

Imagine the following:

A -> B

B is consequent (and subsequent) to A, because A implies B.

How might one describe A relative to B? "Presequent" gets a few search results... but perhaps there's a better-established word?

Another example:

Because it rained, the grass is wet.`

The wet grass is consequent to the rain. How can one make a similar statement about the rain itself?

You could say that the rain is antecedent to the grass getting wet. The Oxford English Dictionary writes that:

A thing or circumstance which goes before or precedes in time or order; often also implying causal relation with its consequent.

So, antecedent is often paired with consequent. They write further that in logic:

Hence, in various special applications, of which the logical and grammatical are the earliest uses of the word in English: Logic. (Opposed to consequent.) The statement upon which any consequence logically depends; hence †(a) The premisses of a syllogism (obs.); (b) The part of a conditional proposition on which the other depends. †(c) By some early logicians the subject and predicate were called antecedent and consequent.

For example, a usage in writing is:

1870 F. C. Bowen Logic v. 128 All Hypothetical Judgments obviously consist of two parts, the first of which is called the Condition or Antecedent.

Precedent also works as an adjective.

The rain is precedent to the wet grass.