Theorem: Execution.Step.Apply.RTC.preserves_tag (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.tag = s₂.tag
Tactic:
induction e
State after:
case refl
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ s✝ : State α
⊢ s✝.tag = s✝.tag

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✝.tag = s₃✝.tag
⊢ s₁✝.tag = s₃✝.tag

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ s✝ : State α
⊢ s✝.tag = s✝.tag
Tactic:
case refl => rfl
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✝.tag = s₃✝.tag
⊢ s₁✝.tag = s₃✝.tag
Tactic:
case trans e _ hi => exact e.preserves_tag ▸ hi
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ : State α
out : Reaction.Output
s₂ s✝ : State α
⊢ s✝.tag = s✝.tag
Tactic:
rfl
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✝.tag = s₃✝.tag
⊢ s₁✝.tag = s₃✝.tag
Tactic:
exact e.preserves_tag ▸ hi
State after:
no goals