Bind congr of forall mem support
OracleComp.bind_congr_of_forall_mem_support
Plain-language statement
Support-aware bind congruence: if two continuations agree on all elements in the support of mx, the resulting bind computations are equal.
Exact Lean statement
theorem bind_congr_of_forall_mem_support (mx : OracleComp spec α) {f g : α → OracleComp spec β}
(h : ∀ x ∈ support mx, f x = g x) : mx >>= f = mx >>= gFormal artifact
Lean source
theorem bind_congr_of_forall_mem_support (mx : OracleComp spec α) {f g : α → OracleComp spec β} (h : ∀ x ∈ support mx, f x = g x) : mx >>= f = mx >>= g := by induction mx using OracleComp.inductionOn with | pure a => simpa only [monad_norm] using h a (by simp) | query_bind q k ih => change (query q : OracleComp spec _) >>= (fun u => k u >>= f) = (query q : OracleComp spec _) >>= (fun u => k u >>= g) exact bind_congr fun u => ih u fun x hx => h x ((mem_support_bind_iff _ _ _).mpr ⟨u, by simp, hx⟩)- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/EvalDist.lean:161-170
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