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 <lhs>\n _ = <rhs> := <proof>. This is useful for aligning relation symbols, especially on longer: identifiers:

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

                                          calc works as a term, as a tactic or as a conv tactic.

                                          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 <lhs>\n _ = <rhs> := <proof>. This is useful for aligning relation symbols, especially on longer: identifiers:

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

                                            calc works as a term, as a tactic or as a conv tactic.

                                            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 <lhs>\n _ = <rhs> := <proof>. This is useful for aligning relation symbols, especially on longer: identifiers:

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

                                              calc works as a term, as a tactic or as a conv tactic.

                                              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 <params> := D_1, ..., D_n
                                                                                                                            

                                                                                                                            into

                                                                                                                            class C <params> 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 : Type ?u.14} [Monad m] => Lean.Loop.forIn }
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                                                                                                                                                  Unexpander for the { x } notation.

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                                                                                                                                                    Unexpander for the { x, y, ... } notation.

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