grammar - "Four plus two equals six" (or "is equal to six" or "is six")

You write

4 + 2 = 6

and say "four plus two equals (or is equal to or is) six."

In the question “Is equal to” or “equals”, I read the following comment:

Equals is equal being a verb, in the present tense. Is equal to is equal being a predicate adjective, with its auxiliary verb in the present tense. English is full of pairs like this, useful if one needs an extra syllable. [...] – John Lawler Jun 16 at 16:18

I am thoroughly confused about the bit "Is equal to is equal being a predicate adjective, with its auxiliary verb in the present tense". Is the verb in the present tense the word is? and is to the predicate with the adjective being equal?

Also, does the word is represent a verb in the present tense in the phrase, "four plus two is six"?

Finally, could you please provide another example that is useful if one needs an extra syllable.

Yes, I understand that they all mean the same thing. What I'm looking for is a grammatical syntax analysis with more examples, since, as John Lawler says, "English is full of pairs like this, useful if one needs an extra syllable."

(As an aside, I once read that this symbol "=" is called an "equals sign" in British English and is called an "equal sign" in American English. A related post can be found here.)

Answer

If one wants a complete grammatical analysis, one should be prepared for the view that be equal to is a transitive multi-word verb, a single lexeme.

("A lexeme is a unit of lexical meaning, which exists regardless of any inflectional endings it may have or the number of words it may contain. Thus, fibrillate, rain cats and dogs, and come in are all lexemes, as are elephant, jog, cholesterol, happiness, put up with, face the music, and hundreds of thousands of other meaningful items in English. The headwords in a dictionary are all lexemes."
(David Crystal, The Cambridge Encyclopedia of the English Language, 2nd ed. Cambridge University Press, 2003) )

The fact that is equal to etc can readily be substituted by equals etc strongly supports the multi-word single-lexeme analysis. It then becomes arguable whether it is helpful to try to analyse within the fixed expression (along the lines: is equal more closely bound to the 'verb' or the 'preposition'? if the 'adjective'-'preposition' binding is tight, is to better analysed as a particle?).

Of course, the verb-form is not invariant: So, the left-hand side must be equal to the right-hand side.

Also, be equal to meaning measure up to (the demands of) is not synonymous with equal:

Do you think he is equal to the task?

*Do you think he equals the task?