openAI-math-dataset / lean /OAI /Combinatorics /EditApproximation /Geometry /ChargedTerminalCost.lean
| import OAI.Combinatorics.EditApproximation.Geometry.ChargedQueryProgress | |
| import OAI.Combinatorics.EditApproximation.Geometry.ChargedIndexCost | |
| import OAI.Combinatorics.EditApproximation.Probability.FiniteQueryCostOrder | |
| namespace OAI | |
| /-! Warmup and terminal queries have no same-index requests. Their | |
| charged seed reads strictly decrease the pass index, including coarse | |
| entries at pass zero. -/ | |
| namespace EditApproximation | |
| theorem chargedWarmupQuery_same_cost_zero {α : Type*} [DecidableEq α] {M J passes copies T S : ℕ} | |
| (source target : List α) (N P F : ℕ) (factor : ℕ → ℚ) (multiplier : ℕ → ℕ) | |
| (parent : {r : PhysicalTableRequest M J target.length // r.Bounded passes copies T S}) (oracle) : | |
| (chargedWarmupQuery source target N P F factor multiplier parent).cost oracle | |
| (fun child => chargedSameWeight (Sum.inr parent) child.val) = 0 := by | |
| apply FiniteQuery.cost_eq_zero_of_keys | |
| intro key hk | |
| have h := chargedWarmupQuery_keys_earlier source target N P F factor multiplier parent oracle key hk | |
| exact ite_eq_right (not_not_intro h.2) | |
| theorem chargedInitialQuery_same_cost_zero {α : Type*} [DecidableEq α] {M J passes copies T S : ℕ} | |
| (source target : List α) (N P F : ℕ) (factor : ℕ → ℚ) (multiplier : ℕ → ℕ) | |
| (parent : {r : PhysicalTableRequest M J target.length // r.Bounded passes copies T S}) (oracle) : | |
| (physicalInitialQuery source target N P F (factor parent.val.pass) | |
| (chargedSeedQuery N multiplier parent) (parent.val.node, parent.val.state)).cost oracle | |
| (fun child => chargedSameWeight (Sum.inr parent) child.val) = 0 := by | |
| apply FiniteQuery.cost_eq_zero_of_keys | |
| have hkeys := physicalInitialQuery_keys_all source target N P F (factor parent.val.pass) | |
| (chargedSeedQuery N multiplier parent) parent.val.node parent.val.state oracle | |
| (fun key => key.val.index < ChargedPhysicalRequest.index (Sum.inr parent)) | |
| (fun q key hk => (chargedSeedQuery_keys_earlier N multiplier parent (parent.val.node, q) oracle key hk).2) | |
| intro key hk | |
| exact ite_eq_right (not_not_intro (hkeys key hk)) | |
| end EditApproximation | |
| end OAI | |