leanprover / leanprover/lean4

Confusing goal with unfinished `have`

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enhancement P-low server
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Lean
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Description

Description

In the following unfinished proof:

example : ∃n, n < 1 := by
   have h : 0 < 1 := 
                   --^ cursor here
   exact ⟨0, h⟩

the goal state shows up as

h : 0 < 1
⊢ ∃ n, n < 1

with 0 < 1 as the assumption. To see the "real" goal ⊢ 0 < 1 we have to write by. This is confusing for beginners, since really at that cursor there is no goal state at all -- one should produce a term. So I suggest we show an expected type there rather than a goal state.

Versions

8df2b07

Contributor guide

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start with the unfinished-proof example in the issue and trace how Lean presents the state at the cursor after have h : 0 < 1 :=. The work is done when that position reports an expected type rather than the surrounding theorem goal, while the by form continues to show a goal state.

Written by the indexing model from the issue text.

Assessment

Domain
compilers
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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