[{"type":"thinking","thinking":"Line 286: `Real.log_pos (by linarith)` in hloglogT's hlogTpos — the goal is `1 < √80000 + 1` and linarith has only hT (upper bound) — needs √80000 > 0 i.e. sqrt80000_ge (282 ≤ √80000) which is NOT in context at that point (I declared sqrt80000_ge usage later via hlogTge1's linarith [sqrt80000_ge]). At line 286 the context lacks a lower bound on √80000. Fix: `Real.log_pos (by linarith [sqrt80000_ge])`.\n\nLine 305 similar (hloglogT2's hlogT2pos): `Real.log_pos (by linarith)` needs 1 < √80000+1+2 ⟸ √80000 > −2 — from sqrt_nonneg: actually √80000 ≥ 0 gives √80000+1+2 ≥ 3 > 1 — but is sqrt_nonneg in context? hTpos : 0 < √80000+1 was declared — linarith can use it: 0 < √80000+1 ⟹ √80000+1+2 > 1 ✓. Hmm — but the error at 305 shows context up to hloglogT... and the failure — wait line 305 is hlogT2pos : 0 < Real.log (√80000+1+2) := Real.log_pos (by linarith) — goal of by linarith: 1 < √80000+1+2. Context has hTpos : 0 < √80000+1 — from which √80000+1+2 > 3 > 1 ✓ linarith should close. Hmm but the error at 305 says linarith failed... with a✝ : √80000+1 ≤ 1 — that's the negation of `1 < √80000+1`?? No wait, the first error (286) has a✝ : √80000 + 1 ≤ 1 ⊢ False — the goal being proved is 1 < √80000+1 — linarith failed because no lower bound on √80000 in context (hTpos : 0 < √80000+1 IS in context! From hTpos: √80000 > −1, so √80000+1 > 0 — but we need > 1, i.e. √80000 > 0 — hTpos gives √80000 + 1 > 0 only ⟹ √80000 > −1. NOT enough! Need sqrt80000_ge (282 ≤ √80000) or sqrt_pos. Right — hTpos is too weak. Fix both: (by linarith [sqrt80000_ge]).\n\nSecond error at 305:24 — that's hlogT2pos in hloglogT2 block: Real.log_pos (by linarith): goal 1 < √80000+1+2 ⟸ √80000 > −2: from hTpos (0 < √80000+1) — √80000+1+2 > 1 ⟺ √80000 > −2 ✓ hTpos gives √80000 > −1 ✓ sufficient! Hmm but error persists... wait the error message at 305 shows context WITHOUT hTpos? No — the context shows hT, hTpos at top ✓. Let me recheck: 305:24 error context (second dump) is truncated — it ends at hloglogT. The failing goal there: hlogT2pos's `by linarith` for `1 < √80000 + 1 + 2`? With hTpos : 0 < √80000+1: √80000+1+2 = (√80000+1)+2 > 0+2 = 2 > 1 ✓ linarith SHOULD find it. Unless the failing linarith is elsewhere in that block... The error line 305:24 — let me count lines. Actually let me just fix both Real.log_pos calls to include sqrt80000_ge and recompile to see remaining errors.","signature":""},{"type":"text","text":"The `Real.log_pos` calls need the sqrt lower bound in scope. Fixing both."},{"type":"tool_use","id":"Edit_156","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiBasePoints.lean","old_string":"  have hloglogT : Real.log (Real.log (Real.sqrt 80000 + 1)) ≤ (1.75 : ℝ) := by\n    have hlogTpos : (0 : ℝ) < Real.log (Real.sqrt 80000 + 1) :=\n      Real.log_pos (by linarith)","new_string":"  have hloglogT : Real.log (Real.log (Real.sqrt 80000 + 1)) ≤ (1.75 : ℝ) := by\n    have hlogTpos : (0 : ℝ) < Real.log (Real.sqrt 80000 + 1) :=\n      Real.log_pos (by linarith [sqrt80000_ge])"},"extra_content":null},{"type":"tool_use","id":"Edit_157","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiBasePoints.lean","old_string":"    have hlogT2pos : (0 : ℝ) < Real.log (Real.sqrt 80000 + 1 + 2) :=\n      Real.log_pos (by linarith)\n    have h := Real.log_le_log hlogT2pos (le_trans hlogT2 h175big)","new_string":"    have hlogT2pos : (0 : ℝ) < Real.log (Real.sqrt 80000 + 1 + 2) :=\n      Real.log_pos (by linarith [sqrt80000_ge])\n    have h := Real.log_le_log hlogT2pos (le_trans hlogT2 h175big)"},"extra_content":null}]