0specs/FD-implies-DATA-refine/proofs/3377954158inj ⊦ ei + el = ei0 + el0 ↔ ei = ei0 ∧ el = el001inj-proofinj-proof-infotrans ⊦ el < el0 ∧ el0 < el1 → el < el101trans-prooftrans-proof-infoless-01 ⊦ el0 < ei + el ↔ el0 = el ∨ el0 < el01less-01-proofless-01-proof-infoelim ⊦ el ≠ [] → (ei = hd el ∧ el0 = tl el ↔ el = ei + el0)01elim-proofelim-proof-infoCons ⊦ (ei + el) + el3 = ei + (el + el3)01Cons-proofCons-proof-infoTwo ⊦ ei + ei1 = ei ' + ei1 '01Two-proofTwo-proof-inforefinement ⊦ ¬ div_A([]) → ¬ div_C([]) ∧ (∀ g⊥ω, g⊥ω'. CSEM^(el)(g⊥ω, g⊥ω') → ASEM^(el)(g⊥ω, g⊥ω'))omega-refine41100refinement-proofrefinement-proof-infoomega-refine¬ div_A([]), ¬ div_C([]), CSEM^(el)(E ', ω) ⊦ ASEM^(el)(E ', ω)24omega-refine-proofomega-refine-proof-infolocalsimp