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← Session 27 — ii′-5c/5d: Davenport disc + FE-reflection bounds

#1381 assistant 2026-08-23 06:40:14.980 UTC · 1936→714 tok open ⤢
thinking (1530 chars)
HUGE progress — everything through hmid now compiles (hEM, hconv, hsum, hint, harctan, hrem, hboundary, hmid all in context, no errors). Two errors left, both in hv1's calc: 1. Line 897: `apply add_le_add_right` for `3 / v.im^2 + 1/4 ≤ 3/4 + 1/4` — per the flipped convention, add_le_add_right : b ≤ c → ∀ a, a + b ≤ a + c — so `add_le_add_right (h : 3/v.im² ≤ 3/4) (1/4)` gives 1/4 + 3/v.im² ≤ 1/4 + 3/4 — the a goes on the LEFT. My goal: 3/v.im² + 1/4 ≤ 3/4 + 1/4 — needs (h) (a) with a appended RIGHT: that's add_le_add_LEFT per this Mathlib (h : b ≤ c → (a) → b + a ≤ c + a)? From the earlier error: add_le_add_left produced `|w.arg| + ?m ≤ π + ?m` — i.e., add_le_add_left (h : b ≤ c) (a) : b + a ≤ c + a ✓. So use add_le_add_left here: ``` apply add_le_add_left -- wait: `apply` with the _ argument... rw [div_le_div_iff₀ ...]; nlinarith ``` hmm — I wrote `apply add_le_add_right` then the div proof as a NEW goal — the apply produced goal 3/v.im² ≤ 3/4. With add_le_add_left it should match: add_le_add_left (h : b ≤ c) (a : α) : b + a ≤ c + a — apply to goal 3/v.im² + 1/4 ≤ 3/4 + 1/4: b := 3/v.im², c := 3/4, a := 1/4 ✓ leaving goal 3/v.im² ≤ 3/4 ✓. Just swap right→left. 2. Line 920: `div_le_div_left` unknown identifier. Need the current name: candidates: `div_le_div_iff_of_pos_left`? journal-024 mentioned "div_le_div_iff_of_pos_right/left (renames)". Let me check: `div_le_div_iff_of_pos_left`? or `div_le_div_left` renamed to `div_le_div_iff_left`? Let me grep for the iff form: "a / b ≤ a / c ↔".
Just two fixes left in hv1. Checking the div_le_div_left rename.
tool: Bash
input
{
  "command": "cd /d/Python/Quantum/zeta-23-lean/.lake/packages/mathlib && grep -rn \"theorem div_le_div_iff_of_pos_left\\|theorem div_le_div_left\\|theorem div_le_div_iff_left\" Mathlib/Algebra/Order/ 2>/dev/null | head -4",
  "description": "Find the div_le_div_left current name"
}
raw content_json (database row)
[{"type":"thinking","thinking":"HUGE progress — everything through hmid now compiles (hEM, hconv, hsum, hint, harctan, hrem, hboundary, hmid all in context, no errors). Two errors left, both in hv1's calc:\n\n1. Line 897: `apply add_le_add_right` for `3 / v.im^2 + 1/4 ≤ 3/4 + 1/4` — per the flipped convention, add_le_add_right : b ≤ c → ∀ a, a + b ≤ a + c — so `add_le_add_right (h : 3/v.im² ≤ 3/4) (1/4)` gives 1/4 + 3/v.im² ≤ 1/4 + 3/4 — the a goes on the LEFT. My goal: 3/v.im² + 1/4 ≤ 3/4 + 1/4 — needs (h) (a) with a appended RIGHT: that's add_le_add_LEFT per this Mathlib (h : b ≤ c → (a) → b + a ≤ c + a)? From the earlier error: add_le_add_left produced `|w.arg| + ?m ≤ π + ?m` — i.e., add_le_add_left (h : b ≤ c) (a) : b + a ≤ c + a ✓. So use add_le_add_left here:\n```\n        apply add_le_add_left  -- wait: `apply` with the _ argument...\n        rw [div_le_div_iff₀ ...]; nlinarith\n```\nhmm — I wrote `apply add_le_add_right` then the div proof as a NEW goal — the apply produced goal 3/v.im² ≤ 3/4. With add_le_add_left it should match: add_le_add_left (h : b ≤ c) (a : α) : b + a ≤ c + a — apply to goal 3/v.im² + 1/4 ≤ 3/4 + 1/4: b := 3/v.im², c := 3/4, a := 1/4 ✓ leaving goal 3/v.im² ≤ 3/4 ✓. Just swap right→left.\n\n2. Line 920: `div_le_div_left` unknown identifier. Need the current name: candidates: `div_le_div_iff_of_pos_left`? journal-024 mentioned \"div_le_div_iff_of_pos_right/left (renames)\". Let me check: `div_le_div_iff_of_pos_left`? or `div_le_div_left` renamed to `div_le_div_iff_left`? Let me grep for the iff form: \"a / b ≤ a / c ↔\".","signature":""},{"type":"text","text":"Just two fixes left in hv1. Checking the div_le_div_left rename."},{"type":"tool_use","id":"Bash_128","name":"Bash","input":{"command":"cd /d/Python/Quantum/zeta-23-lean/.lake/packages/mathlib && grep -rn \"theorem div_le_div_iff_of_pos_left\\|theorem div_le_div_left\\|theorem div_le_div_iff_left\" Mathlib/Algebra/Order/ 2>/dev/null | head -4","description":"Find the div_le_div_left current name"},"extra_content":null}]