Theorem: Execution.Instantaneous.Step.TC.preserves_nontrivial (ReactorModel/Execution/Theorems/Grouped/Instantaneous.lean)

State before:
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
n : State.Nontrivial s₁
e : s₁ ↓ᵢ+ s₂
⊢ State.Nontrivial s₂
Tactic:
induction e
State after:
case single
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ : State α
a✝ : s₁✝ ↓ᵢ s₂✝
n : State.Nontrivial s₁✝
⊢ State.Nontrivial s₂✝

case trans
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ s₃✝ : State α
a✝¹ : s₁✝ ↓ᵢ s₂✝
a✝ : s₂✝ ↓ᵢ+ s₃✝
a_ih✝ : State.Nontrivial s₂✝ → State.Nontrivial s₃✝
n : State.Nontrivial s₁✝
⊢ State.Nontrivial s₃✝

State before:
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ : State α
e : s₁✝ ↓ᵢ s₂✝
n : State.Nontrivial s₁✝
⊢ State.Nontrivial s₂✝
Tactic:
case single e     => exact e.preserves_nontrivial n
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ s₃✝ : State α
e : s₁✝ ↓ᵢ s₂✝
a✝ : s₂✝ ↓ᵢ+ s₃✝
hi : State.Nontrivial s₂✝ → State.Nontrivial s₃✝
n : State.Nontrivial s₁✝
⊢ State.Nontrivial s₃✝
Tactic:
case trans e _ hi => exact hi $ e.preserves_nontrivial n
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ : State α
e : s₁✝ ↓ᵢ s₂✝
n : State.Nontrivial s₁✝
⊢ State.Nontrivial s₂✝
Tactic:
exact e.preserves_nontrivial n
State after:
no goals

State before:
α : Type
inst✝ : Hierarchical α
s₁ s₂ : State α
rcn : ID
s₁✝ s₂✝ s₃✝ : State α
e : s₁✝ ↓ᵢ s₂✝
a✝ : s₂✝ ↓ᵢ+ s₃✝
hi : State.Nontrivial s₂✝ → State.Nontrivial s₃✝
n : State.Nontrivial s₁✝
⊢ State.Nontrivial s₃✝
Tactic:
exact hi $ e.preserves_nontrivial n
State after:
no goals