Documentation

Lean.Meta.Tactic.Grind.Propagate

Propagates equalities for a conjunction a ∧ b based on the truth values of its components a and b. This function checks the truth value of a and b, and propagates the following equalities:

  • If a = True, propagates (a ∧ b) = b.
  • If b = True, propagates (a ∧ b) = a.
  • If a = False, propagates (a ∧ b) = False.
  • If b = False, propagates (a ∧ b) = False.
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    Propagates truth values downwards for a conjunction a ∧ b when the expression itself is known to be True.

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      Propagates equalities for a disjunction a ∨ b based on the truth values of its components a and b. This function checks the truth value of a and b, and propagates the following equalities:

      • If a = False, propagates (a ∨ b) = b.
      • If b = False, propagates (a ∨ b) = a.
      • If a = True, propagates (a ∨ b) = True.
      • If b = True, propagates (a ∨ b) = True.
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        Propagates truth values downwards for a disjuction a ∨ b when the expression itself is known to be False.

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          Propagates equalities for a negation Not a based on the truth value of a. This function checks the truth value of a and propagates the following equalities:

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            Propagates truth values downwards for a negation expression Not a based on the truth value of Not a. This function performs the following:

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              Propagates Eq upwards

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                Propagates Eq downwards

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                  Propagates HEq downwards

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                    Propagates HEq upwards

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                      Propagates ite upwards

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                        Propagates dite upwards

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