Documentation

Lean.Parser.Tactic

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              match performs case analysis on one or more expressions. See Induction and Recursion. The syntax for the match tactic is the same as term-mode match, except that the match arms are tactics instead of expressions.

              example (n : Nat) : n = n := by
                match n with
                | 0 => rfl
                | i+1 => simp
              
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                  Introduces one or more hypotheses, optionally naming and/or pattern-matching them. For each hypothesis to be introduced, the remaining main goal's target type must be a let or function type.

                  • intro by itself introduces one anonymous hypothesis, which can be accessed by e.g. assumption. It is equivalent to intro _.
                  • intro x y introduces two hypotheses and names them. Individual hypotheses can be anonymized via _, given a type ascription, or matched against a pattern:
                    -- ... ⊢ α × β → ...
                    intro (a, b)
                    -- ..., a : α, b : β ⊢ ...
                    
                  • intro rfl is short for intro h; subst h, if h is an equality where the left-hand or right-hand side is a variable.
                  • Alternatively, intro can be combined with pattern matching much like fun:
                    intro
                    | n + 1, 0 => tac
                    | ...
                    
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