Algebra · medium

Statement, exactly as the model and Lean see it

theorem lg_target (x y : ℝ) (h₁ : x + y = 10) (h₂ : x - y = 4) : x * y = 21 := by

Source: Written for LeanGraph, reference proof certified
Premises used by the reference proof: 53

Traces

Each configuration's full record: what was retrieved, what the model wrote, what Lean said back.

Verified0 model calls · 7 Lean checks · $0.00000

Attempts

attempt 1Wrong tactic

Proof

rfl

What Lean printed (this is all the model sees on repair)

4:2: error: Tactic `rfl` failed: The left-hand side
  x * y
is not definitionally equal to the right-hand side
  21

x y : ℝ
h₁ : x + y = 10
h₂ : x - y = 4
⊢ x * y = 21

attempt 2Other

Proof

decide

What Lean printed (this is all the model sees on repair)

4:2: error: Expected type must not contain free variables
  x * y = 21

Hint: Use the `+revert` option to automatically clean up and revert free variables

attempt 3Valid but mathematically wrong
Proof
```
norm_num
```
What Lean printed (this is all the model sees on repair)
```
3:79: error: unsolved goals
x y : ℝ
h₁ : x + y = 10
h₂ : x - y = 4
⊢ x * y = 21
```
attempt 4Wrong tactic
Proof
```
simp
```
What Lean printed (this is all the model sees on repair)
```
4:2: error: `simp` made no progress
```

attempt 5Wrong tactic

Proof

ring

What Lean printed (this is all the model sees on repair)

4:2: info: Try this:
  [apply] ring_nf
  
  The `ring` tactic failed to close the goal. Use `ring_nf` to obtain a normal form.
    
  Note that `ring` works primarily in *commutative* rings. If you have a noncommutative ring, abelian group or module, consider using `noncomm_ring`, `abel` or `module` instead.
3:79: error: unsolved goals
x y : ℝ
h₁ : x + y = 10
h₂ : x - y = 4
⊢ x * y = 21

attempt 6Wrong tactic

Proof

linarith

What Lean printed (this is all the model sees on repair)

4:2: error: linarith failed to find a contradiction
case h1
x y : ℝ
h₁ : x + y = 10
h₂ : x - y = 4
a✝ : x * y < 21
⊢ False
failed

attempt 7Verified
Proof
```
nlinarith
```

Verified proof

theorem lg_target (x y : ℝ) (h₁ : x + y = 10) (h₂ : x - y = 4) : x * y = 21 := by
  nlinarith

Axioms used: propext, Classical.choice, Quot.sound

Reference proof

The proof we wrote and certified before any model ran.

have hx : x = 7 := by linarith
have hy : y = 3 := by linarith
subst hx hy
norm_num