Theorem: Execution.Step.Apply.RTC.equiv (ReactorModel/Execution/Theorems/Step/Apply.lean)

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ : State α
e : s₁ -[out]→ s₂
⊢ s₁.rtr ≈ s₂.rtr
Tactic:
induction e
State after:
case refl
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ s✝ : State α
⊢ s✝.rtr ≈ s✝.rtr

case trans
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ : State α
hd✝ : Change
s₁✝ s₂✝ : State α
tl✝ : Reaction.Output
s₃✝ : State α
a✝¹ : s₁✝ -[hd✝]→ s₂✝
a✝ : s₂✝ -[tl✝]→ s₃✝
a_ih✝ : s₂✝.rtr ≈ s₃✝.rtr
⊢ s₁✝.rtr ≈ s₃✝.rtr

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ s✝ : State α
⊢ s✝.rtr ≈ s✝.rtr
Tactic:
case refl => exact .refl _
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ : State α
hd✝ : Change
s₁✝ s₂✝ : State α
tl✝ : Reaction.Output
s₃✝ : State α
e : s₁✝ -[hd✝]→ s₂✝
a✝ : s₂✝ -[tl✝]→ s₃✝
hi : s₂✝.rtr ≈ s₃✝.rtr
⊢ s₁✝.rtr ≈ s₃✝.rtr
Tactic:
case trans e _ hi => exact Equivalent.trans e.equiv hi
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ s✝ : State α
⊢ s✝.rtr ≈ s✝.rtr
Tactic:
exact .refl _
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ : State α
hd✝ : Change
s₁✝ s₂✝ : State α
tl✝ : Reaction.Output
s₃✝ : State α
e : s₁✝ -[hd✝]→ s₂✝
a✝ : s₂✝ -[tl✝]→ s₃✝
hi : s₂✝.rtr ≈ s₃✝.rtr
⊢ s₁✝.rtr ≈ s₃✝.rtr
Tactic:
exact Equivalent.trans e.equiv hi
State after:
no goals