établir

The French verb "établir" means "to establish," "to set up," or "to put in place." It involves creating something that was not there before or formalizing a situation, fact, or system.

Meanings and uses:

1. To establish something tangible or institutional:
   Établir une entreprise — to set up a business
   Établir une école — to establish a school

2. To formalize or set down rules, laws, or agreements:
   Établir un contrat — to draw up a contract
   Établir une règle — to establish a rule

3. To prove or demonstrate:
   Établir la vérité — to establish the truth
   Établir un fait — to establish a fact

4. To set up a formal record or document:
   Établir un rapport — to prepare a report

Synonyms and differences:

• Créer — "to create," focuses more on creation or bringing into existence something new, less formal than "établir."
  Créer une entreprise (to create a business) vs. Établir une entreprise (to establish a business in a formal/systematic way).

• Installer — "to install" or "to set up," often used for physical placement or arranging things, less abstract.
  Installer du matériel (to install equipment) vs. Établir un système (to establish a system).

• Instituer — to institute or establish (often official bodies, laws, or ceremonies), a bit more formal and legalistic than "établir."
  Instituer une taxe (to institute a tax) vs. Établir une taxe (to establish, sometimes more general).

• Fixer — to fix, set, or determine (often referring to dates, prices, or rules), focuses more on determination.
  Fixer une date (to set a date) vs. Établir un échéancier (to establish a schedule).

Summary: "Établir" generally implies putting something in place formally or officially, making it lasting or recognized, whether it be a company, a rule, a fact, or a document.