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How many mortal sins did/does Satan do? Did Satan commit just one mortal sin?
Satan lost sanctifying grace by committing the sin of pride alone (not envy, disobedience, or any other sin; cf. Hugon, O.P., Tractatus Dogmatici vol. 1 p. 693, PDF p. 353).
SuΓ‘rez's De angelis lib. 7 cap. 15 (pp. 897-910) goes into much depth regarding the question of "Whether, besides pride, Lucifer committed other sins in via" and whether these were "by diverse acts or by diverse ill-wills of the same [act]."
Does the number of mortal sins increase as he tempts people to commit sin?
cf. Summa Theologica I q. 63 a. 2 "Whether only the sin of pride and envy can exist in an angel?" co.:
omnia peccata in Dæmonibus esse contingit, quia dum homines ad omnia peccata inducunt, omnium peccatorum reatum incurrunt.
all sins are in the demons; since by leading men to sin they incur the guilt of all sins.