7557542bc2
This PR modifies the `structure` syntax so that parents can be named, like in ```lean structure S extends toParent : P ``` **Breaking change:** The syntax is also modified so that the resultant type comes *before* the `extends` clause, for example `structure S : Prop extends P`. This is necessary to prevent a parsing ambiguity, but also this is the natural place for the resultant type. Implements RFC #7099. Will need followup PRs for cleanup after a stage0 update.
27 lines
1 KiB
Text
27 lines
1 KiB
Text
/-- `OrientedCmp cmp` asserts that `cmp` is determined by the relation `cmp x y = .lt`. -/
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class OrientedCmp (cmp : α → α → Ordering) : Prop where
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/-- The comparator operation is symmetric, in the sense that if `cmp x y` equals `.lt` then
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`cmp y x = .gt` and vice versa. -/
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symm (x y) : (cmp x y).swap = cmp y x
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namespace OrientedCmp
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theorem cmp_eq_gt [OrientedCmp cmp] : cmp x y = .gt ↔ cmp y x = .lt := by
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rw [← Ordering.swap_inj, symm]; exact .rfl
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end OrientedCmp
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/-- `TransCmp cmp` asserts that `cmp` induces a transitive relation. -/
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class TransCmp (cmp : α → α → Ordering) : Prop extends OrientedCmp cmp where
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/-- The comparator operation is transitive. -/
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le_trans : cmp x y ≠ .gt → cmp y z ≠ .gt → cmp x z ≠ .gt
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namespace TransCmp
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variable [TransCmp cmp]
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open OrientedCmp
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theorem ge_trans (h₁ : cmp x y ≠ .lt) (h₂ : cmp y z ≠ .lt) : cmp x z ≠ .lt := by
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have := @TransCmp.le_trans _ cmp _ z y x
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simp [cmp_eq_gt] at *
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-- `simp` did not fire at `this`
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exact this h₂ h₁
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