← Session 27 — ii′-5c/5d: Davenport disc + FE-reflection bounds
thinking (1542 chars)
Line 59:17 — the `have h2 := Nat.cast_nonneg (n : ℕ)` — wait the error was "typeclass IsOrderedRing stuck" at 59:17 — hmm, `Nat.cast_nonneg (n : ℕ)` — Nat.cast_nonneg : 0 ≤ (↑n : α) with [OrderedSemiring α] or [IsOrderedRing]... the α is a METAVARIABLE here (no expected type — `have h2 := Nat.cast_nonneg (n : ℕ)` gives h2 : 0 ≤ (↑n : ?α) with ?α unknown!). Right — Nat.cast_nonneg needs the target type; without ascription it's stuck. Fix: `have h2 : (0:ℝ) ≤ (n : ℝ) := Nat.cast_nonneg n`. Same for all the other bare `Nat.cast_nonneg n` haves throughout the file (they're everywhere!). That's the source of MANY stuck typeclasses (lines 146, 162 etc. — same issue: `have h2 := Nat.cast_nonneg n` unascribed). Let me fix ALL of them: ascribe `(0 : ℝ) ≤ (n : ℝ) := Nat.cast_nonneg n`.
Also line 73: linarith [hNR] needs 1 ≤ ↑N not 0 < ↑N: add hN1R : (1:ℝ) ≤ ↑N via exact_mod_cast hN. Fix:
```
· intro M
apply one_div_le_one_div_of_le (by positivity)
have hN1R : (1 : ℝ) ≤ (N : ℝ) := by exact_mod_cast hN
linarith [hN1R]
```
Also hnonneg's h1 (line 58-60): `have h1 : (0:ℝ) < (n:ℝ) + N := by have h2 := Nat.cast_nonneg...; linarith [hNR, h2]` — h2 stuck as above ⟹ linarith fails. Fix with ascription.
And hγ0's direction fix (line ~233): `(by norm_num : (0:ℝ) ≤ 1/2).trans Real.one_half_lt_eulerMascheroniConstant.le`.
And hsplit's `rw [← hker_summ.sum_add_tsum_nat_add N]` — unsolved goals: the beta-redex issue. Fix with simp only [] or convert.
Let me find all the bare `Nat.cast_nonneg` haves and ascribe them.
The recurring issue: bare `Nat.cast_nonneg n` haves leave the target type a metavariable. Fixing all of them plus the other spots.
tool: Bash
input
{
"command": "grep -n \"Nat.cast_nonneg\" /d/Python/Quantum/research/lean/NguyenRH1/NguyenRH1/LiDigammaLeft.lean",
"description": "Find all Nat.cast_nonneg uses"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Line 59:17 — the `have h2 := Nat.cast_nonneg (n : ℕ)` — wait the error was \"typeclass IsOrderedRing stuck\" at 59:17 — hmm, `Nat.cast_nonneg (n : ℕ)` — Nat.cast_nonneg : 0 ≤ (↑n : α) with [OrderedSemiring α] or [IsOrderedRing]... the α is a METAVARIABLE here (no expected type — `have h2 := Nat.cast_nonneg (n : ℕ)` gives h2 : 0 ≤ (↑n : ?α) with ?α unknown!). Right — Nat.cast_nonneg needs the target type; without ascription it's stuck. Fix: `have h2 : (0:ℝ) ≤ (n : ℝ) := Nat.cast_nonneg n`. Same for all the other bare `Nat.cast_nonneg n` haves throughout the file (they're everywhere!). That's the source of MANY stuck typeclasses (lines 146, 162 etc. — same issue: `have h2 := Nat.cast_nonneg n` unascribed). Let me fix ALL of them: ascribe `(0 : ℝ) ≤ (n : ℝ) := Nat.cast_nonneg n`. \n\nAlso line 73: linarith [hNR] needs 1 ≤ ↑N not 0 < ↑N: add hN1R : (1:ℝ) ≤ ↑N via exact_mod_cast hN. Fix:\n```\n · intro M\n apply one_div_le_one_div_of_le (by positivity)\n have hN1R : (1 : ℝ) ≤ (N : ℝ) := by exact_mod_cast hN\n linarith [hN1R]\n```\nAlso hnonneg's h1 (line 58-60): `have h1 : (0:ℝ) < (n:ℝ) + N := by have h2 := Nat.cast_nonneg...; linarith [hNR, h2]` — h2 stuck as above ⟹ linarith fails. Fix with ascription.\n\nAnd hγ0's direction fix (line ~233): `(by norm_num : (0:ℝ) ≤ 1/2).trans Real.one_half_lt_eulerMascheroniConstant.le`.\n\nAnd hsplit's `rw [← hker_summ.sum_add_tsum_nat_add N]` — unsolved goals: the beta-redex issue. Fix with simp only [] or convert.\n\nLet me find all the bare `Nat.cast_nonneg` haves and ascribe them.","signature":""},{"type":"text","text":"The recurring issue: bare `Nat.cast_nonneg n` haves leave the target type a metavariable. Fixing all of them plus the other spots."},{"type":"tool_use","id":"Bash_306","name":"Bash","input":{"command":"grep -n \"Nat.cast_nonneg\" /d/Python/Quantum/research/lean/NguyenRH1/NguyenRH1/LiDigammaLeft.lean","description":"Find all Nat.cast_nonneg uses"},"extra_content":null}]