71942631d7
This PR adds an explanation to the error message when `cases` and `induction` are applied to a term whose type is not an inductive type. For `Prop`, these tactics now suggest the `by_cases` tactic. Example: ``` tactic 'cases' failed, major premise type is not an inductive type Prop Explanation: the 'cases' tactic is for constructor-based reasoning as well as for applying custom cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above type neither is an inductive type nor has a registered theorem. Consider using the 'by_cases' tactic, which does true/false reasoning for propositions. ``` [Zulip discussion](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Improving.20the.20error.20for.20.60cases.20p.60.20when.20.60p.60.20is.20a.20proposition/near/488882682)
55 lines
1.7 KiB
Text
55 lines
1.7 KiB
Text
/-!
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# Tests of the 'cases' tactic
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-/
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/-!
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Error messages when not an inductive type.
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-/
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/--
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error: tactic 'cases' failed, major premise type is not an inductive type
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Prop
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Explanation: the 'cases' tactic is for constructor-based reasoning as well as for applying custom
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cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above
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type neither is an inductive type nor has a registered theorem.
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Consider using the 'by_cases' tactic, which does true/false reasoning for propositions.
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p : Prop
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⊢ True
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-/
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#guard_msgs in
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example (p : Prop) : True := by
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cases p
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/--
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error: tactic 'cases' failed, major premise type is not an inductive type
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Type
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Explanation: the 'cases' tactic is for constructor-based reasoning as well as for applying custom
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cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above
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type neither is an inductive type nor has a registered theorem.
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Type universes are not inductive types, and type-constructor-based reasoning is not possible.
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This is a strong limitation. According to Lean's underlying theory, the only provable
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distinguishing feature of types is their cardinalities.
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α : Type
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⊢ True
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-/
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#guard_msgs in
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example (α : Type) : True := by
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cases α
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/--
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error: tactic 'cases' failed, major premise type is not an inductive type
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Bool → Bool
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Explanation: the 'cases' tactic is for constructor-based reasoning as well as for applying custom
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cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above
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type neither is an inductive type nor has a registered theorem.
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f : Bool → Bool
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⊢ True
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-/
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#guard_msgs in
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example (f : Bool → Bool) : True := by
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cases f
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