15 lines
902 B
Text
15 lines
902 B
Text
theorem perm.perm_erase_dup_of_perm [congr] : ∀ {A : Type} [H : decidable_eq A] {l₁ l₂ : list A}, l₁ ~ l₂ → erase_dup l₁ ~ erase_dup l₂ :=
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λ A H l₁ l₂ p,
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perm_induction_on p nil
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(λ x t₁ t₂ p r,
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decidable.by_cases (λ xint₁, have xint₂ : x ∈ t₂, from mem_of_mem_erase_dup …, … …)
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(λ nxint₁, have nxint₂ : x ∉ t₂, from λ xint₂, … nxint₁, eq.rec … (eq.symm …)))
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(λ y x t₁ t₂ p r,
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decidable.by_cases
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(λ xinyt₁, decidable.by_cases (λ yint₁, …) (λ nyint₁, have nyint₂ : …, from …, …))
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(λ nxinyt₁,
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have xney : x ≠ y, from ne_of_not_mem_cons nxinyt₁,
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have nxint₁ : x ∉ t₁, from not_mem_of_not_mem_cons nxinyt₁,
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have nxint₂ : x ∉ t₂, from λ xint₂, …,
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… …))
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(λ t₁ t₂ t₃ p₁ p₂, trans)
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