Additional `conv`

tactics.

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`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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Elaborator for the `discharge`

tactic.

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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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`with_reducible tacs`

excutes `tacs`

using the reducible transparency setting.
In this setting only definitions tagged as `[reducible]`

are unfolded.

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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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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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`#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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