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docs: more tauto docstring

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Kevin Buzzard
2025-02-15 16:52:55 +00:00
parent 88021db205
commit a59282f10b
1 changed files with 10 additions and 5 deletions
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15
Game/Levels/AdvMultiplication/L03eq_succ_of_ne_zero.lean
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@@ -17,12 +17,12 @@ truth tables).
## Details
`tauto` *does not do magic*! It doesn't know *anything* about addition or multiplication,
it doesn't even know `add_zero`. It doesn't know anything about *numbers*.
What `tauto` knows about is *logic*. I guess it does know one fact about numbers, it
knows that `a = a`. And that's it. But if you have a hypothesis `x < 37`
and another hypothesis `x < 37 → y = 42` and your goal is `y = 42` then `tauto` will
it doesn't even know `add_zero`. The only things that `tauto` knows about numbers
are firstly that `a = a` and secondly that `0 ≠ 1`, `0 ≠ 2`, `1 ≠ 2` and so on.
What `tauto`'s strength is, is *logic*. If you have a hypothesis `x < 37`
and another hypothesis `x < 37 → y + z = 42` and your goal is `y + z = 42` then `tauto` will
solve this goal, because to solve that goal you don't need to know any facts
about numbers, all you need to know is the rules of logic.
about inequalities or addition, all you need to know is the rules of logic.
## Example
@@ -46,6 +46,11 @@ If you have one hypothesis `h : a ≠ a` then `tauto` will solve the goal becaus
## Example
If you have a hypothesis `h : 0 = 1` then `tauto` will solve the goal, because
`tauto` knows `0 ≠ 1` and this is enough to prove `False`, which implies any goal.
## Example
If you have a hypothesis of the form `a = 0 → a * b = 0` and your goal is `a * b ≠ 0 → a ≠ 0`, then
`tauto` will solve the goal, because the goal is logically equivalent to the hypothesis.
If you switch the goal and hypothesis in this example, `tauto` would solve it too.