feat: add antitonicity lemmas for (co)inductive predicates #8940
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nomeata
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wkrozowski
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…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
wkrozowski
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…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
wkrozowski
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Jun 23, 2025
…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
wkrozowski
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Jun 23, 2025
…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
wkrozowski
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Jun 23, 2025
…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
wkrozowski
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to wkrozowski/lean4
that referenced
this pull request
Jun 23, 2025
…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
wkrozowski
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Jun 24, 2025
…r#8940) This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the `least_fixpoint` / `greatest_fixpoint` constructs. For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate `tock `within the coinductive definition of `tick` appear in negative positions. The dual situation applies to the definition of `tock`: ``` mutual def tick : Prop := tock → tick greatest_fixpoint def tock : Prop := tick → tock least_fixpoint end ```
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This PR introduces antitonicity lemmas that support the elaboration of mixed inductive-coinductive predicates defined using the
least_fixpoint/greatest_fixpointconstructs.For instance, the following definition elaborates correctly because all occurrences of the inductively defined predicate
tockwithin the coinductive definition oftickappear in negative positions. The dual situation applies to the definition oftock: