Documentation

Init.NotationExtra

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                  def Lean.expandExplicitBinders (combinatorDeclName : Lake.Name) (explicitBinders : Lean.Syntax) (body : Lean.Syntax) :
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                    def Lean.expandBrackedBinders (combinatorDeclName : Lake.Name) (bracketedExplicitBinders : Lean.Syntax) (body : Lean.Syntax) :
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                                              Step-wise reasoning over transitive relations.

                                              calc
                                                a = b := pab
                                                b = c := pbc
                                                ...
                                                y = z := pyz
                                              

                                              proves a = z from the given step-wise proofs. = can be replaced with any relation implementing the typeclass Trans. Instead of repeating the right- hand sides, subsequent left-hand sides can be replaced with _.

                                              calc
                                                a = b := pab
                                                _ = c := pbc
                                                ...
                                                _ = z := pyz
                                              

                                              It is also possible to write the first relation as \n _ = := . This is useful for aligning relation symbols, especially on longer: identifiers:

                                              calc abc
                                                _ = bce := pabce
                                                _ = cef := pbcef
                                                ...
                                                _ = xyz := pwxyz
                                              

                                              calc has term mode and tactic mode variants. This is the term mode variant.

                                              See Theorem Proving in Lean 4 for more information.

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                                                Step-wise reasoning over transitive relations.

                                                calc
                                                  a = b := pab
                                                  b = c := pbc
                                                  ...
                                                  y = z := pyz
                                                

                                                proves a = z from the given step-wise proofs. = can be replaced with any relation implementing the typeclass Trans. Instead of repeating the right- hand sides, subsequent left-hand sides can be replaced with _.

                                                calc
                                                  a = b := pab
                                                  _ = c := pbc
                                                  ...
                                                  _ = z := pyz
                                                

                                                It is also possible to write the first relation as \n _ = := . This is useful for aligning relation symbols:

                                                calc abc
                                                  _ = bce := pabce
                                                  _ = cef := pbcef
                                                  ...
                                                  _ = xyz := pwxyz
                                                

                                                calc has term mode and tactic mode variants. This is the tactic mode variant, which supports an additional feature: it works even if the goal is a = z' for some other z'; in this case it will not close the goal but will instead leave a subgoal proving z = z'.

                                                See Theorem Proving in Lean 4 for more information.

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                                                                                                                            Apply function extensionality and introduce new hypotheses. The tactic funext will keep applying the funext lemma until the goal target is not reducible to

                                                                                                                              |-  ((fun x => ...) = (fun x => ...))
                                                                                                                            

                                                                                                                            The variant funext h₁ ... hₙ applies funext n times, and uses the given identifiers to name the new hypotheses. Patterns can be used like in the intro tactic. Example, given a goal

                                                                                                                              |-  ((fun x : Nat × Bool => ...) = (fun x => ...))
                                                                                                                            

                                                                                                                            funext (a, b) applies funext once and performs pattern matching on the newly introduced pair.

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                                                                                                                              Expands

                                                                                                                              class abbrev C  := D_1, ..., D_n
                                                                                                                              

                                                                                                                              into

                                                                                                                              class C  extends D_1, ..., D_n
                                                                                                                              attribute [instance] C.mk
                                                                                                                              
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                                                                                                                                  · tac focuses on the main goal and tries to solve it using tac, or else fails.

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                                                                                                                                    Similar to first, but succeeds only if one the given tactics solves the current goal.

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                                                                                                                                      repeat and while notation #

                                                                                                                                      inductive Lean.Loop :
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                                                                                                                                        @[inline]
                                                                                                                                        def Lean.Loop.forIn {β : Type u} {m : Type u → Type v} [Monad m] :
                                                                                                                                        Lean.Loopβ(Unitβm (ForInStep β)) → m β
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                                                                                                                                          @[specialize #[]]
                                                                                                                                          partial def Lean.Loop.forIn.loop {β : Type u} {m : Type u → Type v} [Monad m] (f : Unitβm (ForInStep β)) (b : β) :
                                                                                                                                          m β
                                                                                                                                          instance Lean.instForInLoopUnit {m : Type u_1 → Type u_2} :
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                                                                                                                                          • Lean.instForInLoopUnit = { forIn := fun {β} [Monad m] => Lean.Loop.forIn }
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