theorem
proved
tactic proof
resolutionCell_eq_iff
show as:
view Lean formalization →
formal statement (Lean)
85theorem resolutionCell_eq_iff {c₁ c₂ : C} :
86 ResolutionCell r c₁ = ResolutionCell r c₂ ↔ c₁ ~[r] c₂ := by
proof body
Tactic-mode proof.
87 constructor
88 · intro h
89 have : c₂ ∈ ResolutionCell r c₁ := by
90 rw [h]
91 exact mem_resolutionCell_self r c₂
92 exact (Indistinguishable.symm' r this)
93 · intro h
94 ext c
95 simp [ResolutionCell, Indistinguishable]
96 constructor
97 · intro hc
98 exact Eq.trans hc h
99 · intro hc
100 exact Eq.trans hc (Eq.symm h)
101
102/-- Resolution cells partition the configuration space -/