Si clauses are typical markers of the Spanish conditional:
Y yo creo que si me hubiese quedado viviendo...
And, I believe that if I had stayed living...
Caption 12, Festivaliando - Mono Núñez
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However, sometimes you could use the conditional phrase de + haber + participio:
Y yo creo que de haberme quedado viviendo...
And, I believe that if I had stayed living...
In fact, the construction de + haber + participio (endings -ado, -ido, -to, -so -cho) is based on what in Spanish is known as the conditional compuesto or condidional perfecto (perfect conditional):
Here's an example of the perfect conditional combined with a si clause:
Tal vez, si yo fuera un poco más sensata
Maybe, if I were a bit more sensible
habría inventado una poción
I would have invented a potion
Captions 20-21, Belanova - Tal vez
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And this is how you substitute si with de:
Tal vez, de ser un poco más sensata habría inventado una poción
Maybe, if I were a bit more sensible I would have invented a potion
Just for practice, instead of present subjunctive (yo fuera) let's use past perfect subjunctive:
Tal vez, si yo hubiera sido un poco más sensata habría inventado una poción
Maybe, if I had been a bit more sensible I would have invented a potion
Substitution is as follows:
Tal vez, de haber sido un poco más sensata habría inventado una poción
Maybe, if I had been a bit more sensible I would have invented a potion
This recalls the common phrase de haber sabido (if I had known). It's also common to combine it with direct object pronouns: de haberlo sabido (If I had known of it), de haberlo pensado (if I had thought of it).
But de + infinitive is not always an option. For example, you can't use it instead of the si clause when the conditional refers to an action in the future. You can't use it in the following example:
Voy a ver si alguna quiere jugar conmigo a Nimanji.
I am going to see if anyone wants to play Nimanji with me.
Caption 26, Kikirikí - Animales
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This is because the perfect conditional can only be used to refer to actions in the past. Also have in mind that the perfect conditional is not only used with si clauses, because sometimes the condition for something to happen is left unexpressed or it's inferred only by context:
Yo y mi hermana hemos vivido una vida
My sister and I have lived a life
que no nos habríamos imaginado.
that we wouldn't have imagined.
Captions 68-69, Horno San Onofre - La Historia de la Pastelería
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But if we artificially add a si clause to the previous example, let's say:
Yo y mi hermana hemos vivido una vida que no nos habríamos imaginado [si viviéramos en México]
My sister and I have lived a life that we wouldn't have imagined [if we were living in Mexico]
Then you can make the de + infinitive substitution:
Yo y mi hermana hemos vivido una vida que no nos habríamos imaginado [de vivir en México]
My sister and I have lived a life that we wouldn't have imagined [if we were living in Mexico]