← Session 17 — Lean tier (i): elementary proofs (after crash)
thinking (854 chars)
Line 165:14 — the `le_of_eq (by ring ...)` — isDefEq timeout. The `by ring` proof term's type must be unified with the needed equation `(n*(n−1))/(2*(m:ℝ)^2) = C*(1/↑m.1^2)`; the `(m : ℝ)` vs `(m.1 : ℝ)` mismatch is likely causing expensive defeq (coercion paths: (m : ℝ) for m : subtype might go through a different instance chain, not reducibly equal syntactically). Fix: write everything in terms of (m.1 : ℝ) explicitly to match bern_term_upper's conclusion... wait bern_term_upper n m.1 gives (n:ℝ)*(n−1)/(2*(m.1:ℝ)^2)? bern_term_upper's statement: `... ≤ (n : ℝ) * (n - 1) / (2 * m ^ 2)` with m : ℕ — instantiated with m.1: `(2 * (m.1 : ℝ) ^ 2)`. So the le_trans middle term is (n*(n−1))/(2*(m.1:ℝ)^2). My le_of_eq equation should use (m.1 : ℝ) on the LHS too — I wrote (m : ℝ) which triggers coercion-defeq pain. Fix by using (m.1 : ℝ) everywhere.
The `(m : ℝ)` vs `(m.1 : ℝ)` coercion mismatch is causing a defeq timeout. Fix by using `m.1` consistently.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"old_string": " (le_of_eq (by ring : (n : \u211d) * ((n : \u211d) - 1) / (2 * (m : \u211d) ^ 2) =\n ((n : \u211d) * ((n : \u211d) - 1) / 2) * (1 / ((m.1 : \u211d) ^ 2)))))",
"new_string": " (le_of_eq (by ring : (n : \u211d) * ((n : \u211d) - 1) / (2 * (m.1 : \u211d) ^ 2) =\n ((n : \u211d) * ((n : \u211d) - 1) / 2) * (1 / ((m.1 : \u211d) ^ 2)))))"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Line 165:14 — the `le_of_eq (by ring ...)` — isDefEq timeout. The `by ring` proof term's type must be unified with the needed equation `(n*(n−1))/(2*(m:ℝ)^2) = C*(1/↑m.1^2)`; the `(m : ℝ)` vs `(m.1 : ℝ)` mismatch is likely causing expensive defeq (coercion paths: (m : ℝ) for m : subtype might go through a different instance chain, not reducibly equal syntactically). Fix: write everything in terms of (m.1 : ℝ) explicitly to match bern_term_upper's conclusion... wait bern_term_upper n m.1 gives (n:ℝ)*(n−1)/(2*(m.1:ℝ)^2)? bern_term_upper's statement: `... ≤ (n : ℝ) * (n - 1) / (2 * m ^ 2)` with m : ℕ — instantiated with m.1: `(2 * (m.1 : ℝ) ^ 2)`. So the le_trans middle term is (n*(n−1))/(2*(m.1:ℝ)^2). My le_of_eq equation should use (m.1 : ℝ) on the LHS too — I wrote (m : ℝ) which triggers coercion-defeq pain. Fix by using (m.1 : ℝ) everywhere.","signature":""},{"type":"text","text":"The `(m : ℝ)` vs `(m.1 : ℝ)` coercion mismatch is causing a defeq timeout. Fix by using `m.1` consistently."},{"type":"tool_use","id":"Edit_49","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean","old_string":" (le_of_eq (by ring : (n : ℝ) * ((n : ℝ) - 1) / (2 * (m : ℝ) ^ 2) =\n ((n : ℝ) * ((n : ℝ) - 1) / 2) * (1 / ((m.1 : ℝ) ^ 2)))))","new_string":" (le_of_eq (by ring : (n : ℝ) * ((n : ℝ) - 1) / (2 * (m.1 : ℝ) ^ 2) =\n ((n : ℝ) * ((n : ℝ) - 1) / 2) * (1 / ((m.1 : ℝ) ^ 2)))))"},"extra_content":null}]