Instantiate assoc
ResourceProfile.instantiate_assoc
Plain-language statement
Instantiating symbolic capabilities is associative. Substituting impl₁ into a profile c, and then substituting impl₂ into the resulting profile, is the same as substituting the composite implementation fun k ↦ (impl₁ k).instantiate impl₂ into c directly.
Exact Lean statement
@[simp] lemma instantiate_assoc [AddCommMonoid ω]
(c : ResourceProfile ω κ)
(impl₁ : κ → ResourceProfile ω κ')
(impl₂ : κ' → ResourceProfile ω κ'') :
(c.instantiate impl₁).instantiate impl₂ =
c.instantiate (fun k ↦ (impl₁ k).instantiate impl₂)Formal artifact
Lean source
@[simp] lemma instantiate_assoc [AddCommMonoid ω] (c : ResourceProfile ω κ) (impl₁ : κ → ResourceProfile ω κ') (impl₂ : κ' → ResourceProfile ω κ'') : (c.instantiate impl₁).instantiate impl₂ = c.instantiate (fun k ↦ (impl₁ k).instantiate impl₂) := by have hu : ∀ u : κ →₀ ℕ, ((ofUsage (ω := ω) u).instantiate impl₁).instantiate impl₂ = (ofUsage (ω := ω) u).instantiate (fun k ↦ (impl₁ k).instantiate impl₂) := fun u => by induction u using Finsupp.induction with | zero => simp [instantiate] | @single_add a n u ha hn ih => have hsplit : ofUsage (ω := ω) (Finsupp.single a n + u) = single a n + ofUsage u := by ext <;> simp [ofUsage, single] simp only [hsplit, instantiate_add, instantiate_single, instantiate_nsmul, ih] have hc : c = ofIntrinsic (κ := κ) c.intrinsic + ofUsage (ω := ω) c.usage := by ext <;> simp [ofUsage] rw [hc] simp only [instantiate_add, instantiate_ofIntrinsic, hu]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/QueryTracking/ResourceProfile.lean:273-291
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