← Session 24 — ii′-2…4: swaps, (4.10) design, contour + website roadmap fixes
thinking (686 chars)
The lemma `natCast_floor_eq_intCast_floor` is at ROOT namespace (not Nat.). Fix: use `natCast_floor_eq_intCast_floor hx`. The statement: `(⌊a⌋₊ : R) = ⌊a⌋` — with R = ℝ: (↑⌊x⌋₊ : ℝ) = ↑⌊x⌋ ✓. So in b1_eq_fract_sub_half:
```lean
unfold B1 Int.fract
rw [natCast_floor_eq_intCast_floor hx]
```
After unfold: goal x − ↑⌊x⌋₊ − 1/2 = x − ↑⌊x⌋ − 1/2: rw rewrites ↑⌊x⌋₊ → ↑⌊x⌋ ✓ closes by rfl? The remaining would be syntactic equality ✓ — the earlier error showed the unsolved goal `x - ↑⌊x⌋₊ - 1/2 = x - ↑⌊x⌋ - 1/2` — after the rw it should close via rw's auto-rfl. ✓.
Error 2 (typeclass stuck at 106:71): might cascade from the failed lemma above (B1 mention). Let me fix and recompile.
Root-namespace `natCast_floor_eq_intCast_floor` it is.
tool: Edit
input
{
"replace_all": false,
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiRBound.lean",
"old_string": " unfold B1 Int.fract\n rw [Nat.natCast_floor_eq_intCast_floor hx]",
"new_string": " unfold B1 Int.fract\n rw [natCast_floor_eq_intCast_floor hx]"
}
raw content_json (database row)
[{"type":"thinking","thinking":"The lemma `natCast_floor_eq_intCast_floor` is at ROOT namespace (not Nat.). Fix: use `natCast_floor_eq_intCast_floor hx`. The statement: `(⌊a⌋₊ : R) = ⌊a⌋` — with R = ℝ: (↑⌊x⌋₊ : ℝ) = ↑⌊x⌋ ✓. So in b1_eq_fract_sub_half:\n```lean\n unfold B1 Int.fract\n rw [natCast_floor_eq_intCast_floor hx]\n```\nAfter unfold: goal x − ↑⌊x⌋₊ − 1/2 = x − ↑⌊x⌋ − 1/2: rw rewrites ↑⌊x⌋₊ → ↑⌊x⌋ ✓ closes by rfl? The remaining would be syntactic equality ✓ — the earlier error showed the unsolved goal `x - ↑⌊x⌋₊ - 1/2 = x - ↑⌊x⌋ - 1/2` — after the rw it should close via rw's auto-rfl. ✓.\n\nError 2 (typeclass stuck at 106:71): might cascade from the failed lemma above (B1 mention). Let me fix and recompile.","signature":""},{"type":"text","text":"Root-namespace `natCast_floor_eq_intCast_floor` it is."},{"type":"tool_use","id":"Edit_207","name":"Edit","input":{"replace_all":false,"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiRBound.lean","old_string":" unfold B1 Int.fract\n rw [Nat.natCast_floor_eq_intCast_floor hx]","new_string":" unfold B1 Int.fract\n rw [natCast_floor_eq_intCast_floor hx]"},"extra_content":null}]