[{"type":"thinking","thinking":"Issues:\n1. `simpa using (hsm.add (hasDerivAt_const m 1)).deriv` — simp normalized my stated type `fun x => √x + 1` weirdly: it simplified the TARGET to `deriv sqrt m = ...`?? Wait — \"After simplification, term ... has type deriv (sqrt + fun x => 1) m = (√m)⁻¹ * 2⁻¹ but expected deriv sqrt m = (√m)⁻¹*2⁻¹\". Huh — the expected type after simplification became `deriv sqrt m`?? My stated h1 type is `deriv (fun x => √x + 1) m = 1 / (2 * √m)`. simp simplified `fun x => √x + 1`... to `sqrt`?? That can't be. Oh! I see — simp used the lemma `Real.deriv_sqrt`?? No... Actually `simp` simplified the GOAL type `deriv (fun x => √x + 1) m = 1/(2*√m)` — maybe simp has a lemma that computes `deriv (fun x => √x + 1) m`?? There are simp lemmas for deriv of +const: `deriv_add_const`? If simp simplified LHS `deriv (fun x => √x + 1) m` → `deriv sqrt m`? via deriv_add_const simp lemma... and RHS 1/(2*√m) → (√m)⁻¹ * 2⁻¹. And the term's type simplified to deriv (sqrt + fun x => 1) m = ... The mismatch: Pi.add form `sqrt + fun x => 1` vs `sqrt`. So after simp, target = `deriv sqrt m = (√m)⁻¹*2⁻¹` and provided = `deriv (sqrt + fun x=>1) m = ...`. Need to close the small gap: the term's function is sqrt + const, target's is sqrt. simp's lemma deriv_add_const rewrote the target but NOT the term. Use `simpa only [deriv_add_const, ...]`? Simpler: avoid simpa; build exactly:\n\n```lean\nhave h1 : deriv (fun x => √x + 1) m = 1 / (2 * √m) := by\n  rw [deriv_add_const]   -- deriv (sqrt + const)... hmm name?\n```\nIs there `deriv_add_const : deriv (fun x => f x + c) x = deriv f x`? Let me check name... In Mathlib: `deriv_add_const (hf : DifferentiableAt ℝ f x) : deriv (fun x => f x + c) x = deriv f x`? and `deriv_const_add`. Then rw [deriv_add_const (differentiableAt...)] then exact ((Real.hasDerivAt_sqrt ...)).deriv, then ring normalize? hsm.deriv : deriv sqrt m = 1/(2*√m) ✓ directly!\n\nSo: \n```lean\nhave h1 : deriv (fun x => √x + 1) m = 1 / (2 * √m) := by\n  rw [deriv_add_const hsm.differentiableAt]\n  exact hsm.deriv\n```\nName check needed: `deriv_add_const` exists? grep.\n\n2. Same for hA's h1: \n```lean\nhave h1 : HasDerivAt (fun x => √x + 1) (1 / (2 * √n)) n := by\n  rw? — HasDerivAt version: hasDerivAt_add_const? \n```\nSimpler: `(hsqrt.add_const 1)` — HasDerivAt.add_const : HasDerivAt f f' x → HasDerivAt (fun x => f x + c) f' x ✓ exists (`HasDerivAt.add_const`). And for deriv version: `deriv_add_const (hf : DifferentiableAt ...)`. \n\n3. `hg1.hasDerivAt hmul` — invalid field: EventuallyEq has no hasDerivAt method in this Mathlib version, or the argument order differs. Find the right name: search \"EventuallyEq.hasDerivAt\\|congr_of_eventuallyEq\" in Deriv Basic.\n\nAlso hmul produced function in Pi.mul form `(fun ...) * fun ...` — later rw [hder] replaces LHS deriv... but hder : deriv ((fun...) * fun...) n = ... vs goal deriv (deriv fun n => ...) n — after congr it's fine since hder will be about (deriv g) once congr applied correctly.\n\nLet me grep the congr lemma name.","signature":""},{"type":"text","text":"Three name fixes needed. Checking the exact lemma names."},{"type":"tool_use","id":"Bash_175","name":"Bash","input":{"command":"cd /d/Python/Quantum/zeta-23-lean/.lake/packages/mathlib && grep -rn \"theorem deriv_add_const\\|lemma deriv_add_const\" Mathlib/Analysis/Calculus/Deriv/Add.lean | head -2; grep -rn \"congr_of_eventuallyEq\\|EventuallyEq.hasDerivAt\" Mathlib/Analysis/Calculus/Deriv/Basic.lean Mathlib/Analysis/Calculus/FDeriv/Basic.lean 2>/dev/null | head -5","description":"Check deriv_add_const and congr lemma names"},"extra_content":null}]