[[apply-at-relabeled]] : Correct the misspelled conclusion term.
The [[apply-at-tactic]] tactic applies modus ponens, but, unfortunately, it misspells the conclusion term. That is, the label of the premise term is unchanged when it's type changes to the conclusion type:
BEFORE the tactic application, the premise term correctly labels a witness of the premise type:
hPremise : PremiseType
APPLY the tactic: `apply hPimpliesQ at hP`
AFTER the tactic application, the premise term incorrectly labels a witness of the conclusion type:
h<font color="#ff0000">Premise</font> : ConclusionType
This confusion is corrected by applying the [[rename'-tactic|rename']] tactic immediately after the apply tactic, which corrects the spelling of the conclusion term, as in:
apply hPimpliesQ at hP; rename' (hP : Q) => hQ
So, now the conclusion term has a corrected spelling, as in:
BEFORE the tactic application, the premise term correctly labels a witness of the premise type:
hPremise : PremiseType
APPLY the modified tactic: **apply hPimpliesQ at hP; rename' (hP : Q) => hQ**
AFTER the tactic application, the conclusion term changes from h<font color="#ff0000">Premise</font> to the corrected label, h<font color="#00b050">Conclusion</font>:
h<font color="#00b050">Conclusion</font> : ConclusionType
---
Author: [[dducoff]]
Posted Date: 2026-06-28