Simulate Q caching Oracle cache le
OracleComp.simulateQ_cachingOracle_cache_le
Plain-language statement
simulateQ cachingOracle only grows the cache: for any oa, if z ∈ support ((simulateQ cachingOracle oa).run cache₀) then cache₀ ≤ z.2.
Exact Lean statement
theorem simulateQ_cachingOracle_cache_le {α : Type u}
(oa : OracleComp spec α) (cache₀ : QueryCache spec)
(z : α × QueryCache spec)
(hmem : z ∈ support ((simulateQ cachingOracle oa).run cache₀)) :
cache₀ ≤ z.2Formal artifact
Lean source
theorem simulateQ_cachingOracle_cache_le {α : Type u} (oa : OracleComp spec α) (cache₀ : QueryCache spec) (z : α × QueryCache spec) (hmem : z ∈ support ((simulateQ cachingOracle oa).run cache₀)) : cache₀ ≤ z.2 := by induction oa using OracleComp.inductionOn generalizing cache₀ z with | pure a => simp only [StateT.run, simulateQ_pure] at hmem obtain rfl := hmem exact le_rfl | query_bind t mx ih => simp only [simulateQ_query_bind, StateT.run_bind] at hmem rw [mem_support_bind_iff] at hmem obtain ⟨⟨u, cache_mid⟩, hmid, hrest⟩ := hmem have hle_mid : cache₀ ≤ cache_mid := QueryImpl.withCaching_cache_le _ _ cache₀ _ hmid exact hle_mid.trans (ih _ cache_mid z hrest)- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/QueryTracking/CachingOracle.lean:479-494
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