← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (1369 chars)
Two more errors:
1. **Line 165**: `← Real.sqrt_div hQpos` — pattern `√((9+t²)/(4+t²)) / √?y` not found. The goal is `√(9+t²) / √(4+t²) = √((9+t²)/(4+t²))` — the ← direction of Real.sqrt_div : √(x/y) = √x/√y should rewrite √x/√y → √(x/y) with x := 9+t², y := 4+t². But the error shows the pattern it looked for was `√((9+t²)/(4+t²)) / √?y` — WRONG unification: it unified x := (9+t²)/(4+t²)?? — because hQpos's TYPE is 0 ≤ (9+t²)/(4+t²), so `← Real.sqrt_div hQpos` pins x := (9+t²)/(4+t²)! The ← rewrite uses the provided hypothesis to determine x — with hQpos about the DIVIDED form, x gets pinned to the fraction, not to (9+t²). FIX: don't pin with hQpos — use `← Real.sqrt_div (show (0:ℝ) ≤ 9 + t^2 by positivity)` so x := 9+t²: pattern √x/√?y with x = 9+t² ✓. Or use the symmetric direction: prove √(9+t²)/√(4+t²) = √((9+t²)/(4+t²)) via (Real.sqrt_div (by positivity) (4+t^2)).symm:
```
rw [norm_div, hnormA, hnormB, ← Real.sqrt_div (by positivity : (0:ℝ) ≤ 9 + t ^ 2)]
```
2. **Line 194: `Real.sqrt_exp` unknown**. The correct name: `Real.sqrt_exp` doesn't exist?? Hmm — it's `Real.sqrt_exp : √(Real.exp x) = Real.exp (x / 2)`?? — not found. Search: maybe `Real.sqrt_exp` is in a different namespace or the name is `Real.sqrt_exp_of_pos`... Let me check the actual name: candidates: `Real.sqrt_exp`, `Real.exp_half`, `Real.sqrt_exp'`... Let me grep Mathlib.
Two more name fixes — checking the exact `sqrt(exp)` lemma name in this Mathlib.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/zeta-23-lean && grep -rn \"sqrt.*exp\\|exp.*sqrt\" .lake/packages/mathlib/Mathlib/Analysis/SpecialFunctions/Exp/*.lean .lake/packages/mathlib/Mathlib/Analysis/SpecialFunctions/Sqrt/*.lean 2>/dev/null | grep -i \"theorem\\|lemma\" | head -6",
"description": "Find the sqrt(exp x) lemma name"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Two more errors:\n\n1. **Line 165**: `← Real.sqrt_div hQpos` — pattern `√((9+t²)/(4+t²)) / √?y` not found. The goal is `√(9+t²) / √(4+t²) = √((9+t²)/(4+t²))` — the ← direction of Real.sqrt_div : √(x/y) = √x/√y should rewrite √x/√y → √(x/y) with x := 9+t², y := 4+t². But the error shows the pattern it looked for was `√((9+t²)/(4+t²)) / √?y` — WRONG unification: it unified x := (9+t²)/(4+t²)?? — because hQpos's TYPE is 0 ≤ (9+t²)/(4+t²), so `← Real.sqrt_div hQpos` pins x := (9+t²)/(4+t²)! The ← rewrite uses the provided hypothesis to determine x — with hQpos about the DIVIDED form, x gets pinned to the fraction, not to (9+t²). FIX: don't pin with hQpos — use `← Real.sqrt_div (show (0:ℝ) ≤ 9 + t^2 by positivity)` so x := 9+t²: pattern √x/√?y with x = 9+t² ✓. Or use the symmetric direction: prove √(9+t²)/√(4+t²) = √((9+t²)/(4+t²)) via (Real.sqrt_div (by positivity) (4+t^2)).symm:\n```\n rw [norm_div, hnormA, hnormB, ← Real.sqrt_div (by positivity : (0:ℝ) ≤ 9 + t ^ 2)]\n```\n\n2. **Line 194: `Real.sqrt_exp` unknown**. The correct name: `Real.sqrt_exp` doesn't exist?? Hmm — it's `Real.sqrt_exp : √(Real.exp x) = Real.exp (x / 2)`?? — not found. Search: maybe `Real.sqrt_exp` is in a different namespace or the name is `Real.sqrt_exp_of_pos`... Let me check the actual name: candidates: `Real.sqrt_exp`, `Real.exp_half`, `Real.sqrt_exp'`... Let me grep Mathlib.","signature":""},{"type":"text","text":"Two more name fixes — checking the exact `sqrt(exp)` lemma name in this Mathlib."},{"type":"tool_use","id":"Bash_208","name":"Bash","input":{"command":"cd D:/Python/Quantum/zeta-23-lean && grep -rn \"sqrt.*exp\\|exp.*sqrt\" .lake/packages/mathlib/Mathlib/Analysis/SpecialFunctions/Exp/*.lean .lake/packages/mathlib/Mathlib/Analysis/SpecialFunctions/Sqrt/*.lean 2>/dev/null | grep -i \"theorem\\|lemma\" | head -6","description":"Find the sqrt(exp x) lemma name"},"extra_content":null}]