Project-declaredLean 4.32.1 · mathlib@520045ab

LO First Order Language ORing of mem range encode rel

LO.FirstOrder.Language.ORing.of_mem_range_encode_rel

formal logic metatheory proof theory language

Plain-language statement

TODO: move to Basic/Syntax/Bootstrapping.Language.lean

Exact Lean statement

lemma _root_.LO.FirstOrder.Language.ORing.of_mem_range_encode_rel {k r : ℕ} :
    r ∈ Set.range (Encodable.encode : FirstOrder.Language.Rel ℒₒᵣ k → ℕ) ↔
    (k = 2 ∧ r = 0) ∨ (k = 2 ∧ r = 1)

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

lemma _root_.LO.FirstOrder.Language.ORing.of_mem_range_encode_rel {k r : ℕ} :    r ∈ Set.range (Encodable.encode : FirstOrder.Language.Rel ℒₒᵣ k → ℕ) ↔    (k = 2 ∧ r = 0) ∨ (k = 2 ∧ r = 1) := by  constructor  · rintro ⟨r, rfl⟩    match k, r with    | 2, Language.ORing.Rel.eq => simp; rfl    | 2, Language.ORing.Rel.lt => simp; rfl  · rintro (⟨rfl, rfl⟩ | ⟨rfl, rfl⟩)    · exact ⟨Language.ORing.Rel.eq, rfl⟩    · exact ⟨Language.ORing.Rel.lt, rfl⟩

Project: Foundation
License: Apache-2.0
Commit: 8dcdb3196454
Source: Foundation/FirstOrder/Bootstrapping/Syntax/Language.lean:128-138

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