[[apply-relabeling]] : Correct the mislabeled conclusion term after applying Modus Ponens.
The [[apply-at-tactic|apply-at]] tactic invokes modus ponens, `P → Q, P ⊢ Q`, but unfortunately, it mislabels the conclusion term.
BEFORE the `apply`tactic is invoked, all of the term labels align with their types:
`hPimpQ : P → Q`
`hP : PremiseType`
When the `apply at` tactic is invoked:
`apply hPimpQ at hP`
Then the resulting the premise term mislabels a witness of the conclusion type:
<font color="#ff0000">hP</font> `: Q `
This mislabeling is corrected by applying the [[rename'-tactic|rename']] tactic immediately after the `apply` tactic:
`apply hPimpQ at hP`<font color="#00b050">; rename' (hP : Q) => hQ</font>
So, now the conclusion term has a corrected label:
`hQ : Q`
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**`LeanNotes curator:`** [[dducoff]]
**`Posted Date:`** 2026-08-11