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Theorems · Theorem · logic and foundations

StateTransition.tr_reaches

∀ {σ₁ : Type u_1} {σ₂ : Type u_2} {f₁ : σ₁ → Option σ₁} {f₂ : σ₂ → Option σ₂} {tr : σ₁ → σ₂ → Prop},
  StateTransition.Respects f₁ f₂ tr →
    ∀ {a₁ : σ₁} {a₂ : σ₂},
      tr a₁ a₂ → ∀ {b₁ : σ₁}, StateTransition.Reaches f₁ a₁ b₁ → ∃ b₂, tr b₁ b₂ ∧ StateTransition.Reaches f₂ a₂ b₂
Defined in
Mathlib.Computability.StateTransition
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
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StateTransition.tr_eval · cited by 4StateTransition.tr_evalStateTransition.Reaches₁ · cited by 35StateTransition.Reaches₁StateTransition.Reaches · cited by 15StateTransition.ReachesStateTransition.Respects · cited by 14StateTransition.RespectsRelation.TransGen.to_reflTransGen · cited by 8TransGen.to_reflTransGenRelation.reflTransGen_iff_eq_or_transGen · cited by 6Relation.reflTransGen_iff…StateTransition.tr_reaches₁ · cited by 1StateTransition.tr_reache…StateTransition.tr_reachesCITED BYCITES

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