`ConfigSpace`

definition

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module: IndisputableMonolith.Foundation.CostFromDistinction
domain: Foundation
line: 77 · github
papers citing: none yet

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IndisputableMonolith.Foundation.CostFromDistinction on GitHub at line 77.

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depends on

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formal source

  74carrier `K`, multisets of formulas in a sequent calculus, sets of
  75typed assertions, and so on.
  76-/
  77class ConfigSpace (Config : Type u) where
  78  /-- The empty configuration. -/
  79  emp : Config
  80  /-- Joining two configurations. -/
  81  join : Config → Config → Config
  82  /-- Consistency: the configuration is jointly satisfiable. -/
  83  IsConsistent : Config → Prop
  84  /-- Independence: the two configurations share no predicates. -/
  85  Independent : Config → Config → Prop
  86  /-- Empty configuration is consistent. -/
  87  emp_consistent : IsConsistent emp
  88  /-- Independence is symmetric. -/
  89  independent_symm : ∀ Γ₁ Γ₂, Independent Γ₁ Γ₂ → Independent Γ₂ Γ₁
  90  /-- Empty configuration is independent of every configuration. -/
  91  emp_independent : ∀ Γ, Independent emp Γ
  92  /-- Joining is commutative. -/
  93  join_comm : ∀ Γ₁ Γ₂, join Γ₁ Γ₂ = join Γ₂ Γ₁
  94  /-- Joining is associative. -/
  95  join_assoc : ∀ Γ₁ Γ₂ Γ₃, join (join Γ₁ Γ₂) Γ₃ = join Γ₁ (join Γ₂ Γ₃)
  96  /-- Empty is the join identity on the left. -/
  97  emp_join : ∀ Γ, join emp Γ = Γ
  98  /-- Joining two independent consistent configurations yields a
  99      consistent configuration. -/
 100  consistent_of_join_indep : ∀ Γ₁ Γ₂, Independent Γ₁ Γ₂ →
 101    IsConsistent Γ₁ → IsConsistent Γ₂ → IsConsistent (join Γ₁ Γ₂)
 102  /-- If either side of an independent join is inconsistent, the join
 103      is inconsistent. (Independent inconsistencies do not cancel.) -/
 104  inconsistent_of_join_indep_left : ∀ Γ₁ Γ₂, Independent Γ₁ Γ₂ →
 105    ¬IsConsistent Γ₁ → ¬IsConsistent (join Γ₁ Γ₂)
 106
 107namespace ConfigSpace

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