Mathlib.Tactic.Conv

discharge => tac is a conv tactic which rewrites target p to True if tac is a tactic which proves the goal ⊢ p⊢ p.
discharge without argument returns ⊢ p⊢ p as a subgoal.

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def Mathlib.Tactic.Conv.elabDischargeConv :

Lean.Elab.Tactic.Tactic

Elaborator for the discharge tactic.

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def Mathlib.Tactic.Conv.«command#conv_=>_» :

Lean.ParserDescr

The command #conv tac => e will run a conv tactic tac on e, and display the resulting expression (discarding the proof). For example, #conv rw [true_and] => True ∧ False∧ False displays False. There are also shorthand commands for several common conv tactics:

#whnf e is short for #conv whnf => e
#simp e is short for #conv simp => e
#norm_num e is short for #conv norm_num => e
#push_neg e is short for #conv push_neg => e

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def Mathlib.Tactic.Conv.withReducible :

Lean.ParserDescr

with_reducible tacs excutes tacs using the reducible transparency setting. In this setting only definitions tagged as [reducible] are unfolded.

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def Mathlib.Tactic.Conv.«command#whnf_» :

Lean.ParserDescr

The command #whnf e evaluates e to Weak Head Normal Form, which means that the "head" of the expression is reduced to a primitive - a lambda or forall, or an axiom or inductive type. It is similar to #reduce e, but it does not reduce the expression completely, only until the first constructor is exposed. For example:

open Nat List
set_option pp.notation false
#whnf [1, 2, 3].map succ
-- cons (succ 1) (map succ (cons 2 (cons 3 nil)))
#reduce [1, 2, 3].map succ
-- cons 2 (cons 3 (cons 4 nil))

The head of this expression is the List.cons constructor, so we can see from this much that the list is not empty, but the subterms Nat.succ 1 and List.map Nat.succ (List.cons 2 (List.cons 3 List.nil)) are still unevaluated. #reduce is equivalent to using #whnf on every subexpression.

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def Mathlib.Tactic.Conv.«command#whnfR_» :

Lean.ParserDescr

The command #whnfR e evaluates e to Weak Head Normal Form with Reducible transparency, that is, it uses whnf but only unfolding reducible definitions.

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def Mathlib.Tactic.Conv.«command#simpOnly_=>__» :

Lean.ParserDescr

#simp => e runs simp on the expression e and displays the resulting expression after simplification.
#simp only [lems] => e runs simp only [lems] on e.
The => is optional, so #simp e and #simp only [lems] e have the same behavior. It is mostly useful for disambiguating the expression e from the lemmas.

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