Theorem: LeanSAT.Model.PropAssignment.setMany_union (LeanSAT/Model/PropAssn.lean)

State before:
ν : Type u_1
inst✝ : DecidableEq ν
τ : PropAssignment ν
xs₁ xs₂ : Finset ν
τ' : PropAssignment ν
⊢ setMany τ (xs₁ ∪ xs₂) τ' = setMany (setMany τ xs₁ τ') xs₂ τ'
Tactic:
ext v
State after:
case h
ν : Type u_1
inst✝ : DecidableEq ν
τ : PropAssignment ν
xs₁ xs₂ : Finset ν
τ' : PropAssignment ν
v : ν
⊢ setMany τ (xs₁ ∪ xs₂) τ' v = setMany (setMany τ xs₁ τ') xs₂ τ' v

State before:
case h
ν : Type u_1
inst✝ : DecidableEq ν
τ : PropAssignment ν
xs₁ xs₂ : Finset ν
τ' : PropAssignment ν
v : ν
⊢ setMany τ (xs₁ ∪ xs₂) τ' v = setMany (setMany τ xs₁ τ') xs₂ τ' v
Tactic:
simp [setMany]
State after:
case h
ν : Type u_1
inst✝ : DecidableEq ν
τ : PropAssignment ν
xs₁ xs₂ : Finset ν
τ' : PropAssignment ν
v : ν
⊢ (if v ∈ xs₁ ∨ v ∈ xs₂ then τ' v else τ v) = if v ∈ xs₂ then τ' v else if v ∈ xs₁ then τ' v else τ v

State before:
case h
ν : Type u_1
inst✝ : DecidableEq ν
τ : PropAssignment ν
xs₁ xs₂ : Finset ν
τ' : PropAssignment ν
v : ν
⊢ (if v ∈ xs₁ ∨ v ∈ xs₂ then τ' v else τ v) = if v ∈ xs₂ then τ' v else if v ∈ xs₁ then τ' v else τ v
Tactic:
aesop
State after:
no goals