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theorem proved term proof

current_chain_distinct

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formal statement (Lean)

 142theorem current_chain_distinct : (13 : ℕ) ≠ 11 ∧ 11 ≠ 6 ∧ 6 ≠ 8 ∧ 13 ≠ 6 ∧ 13 ≠ 8 ∧ 11 ≠ 8 := by

proof body

Term-mode proof.

 143  refine ⟨?_, ?_, ?_, ?_, ?_, ?_⟩ <;> norm_num
 144
 145/-! ## Constraint 4: The Unique Fully-Integer-Chain Containing E±1
 146
 147One natural structural filter: the chain should contain both "edge plus one"
 148(E+1 = 13) and "edge minus one" (E-1 = 11). These are the simplest
 149symmetric deformations of the edge count E = 12.
 150
 151Under this filter, the remaining two values must sum to 21 - 13 - 11 = ...
 152wait, that over-constrains. Let me redo:
 153
 154If two of the four values are E±1, and the cyclic chain structure is
 155(E+1, E-1, ?, ?) ending back at E+1, then the middle pair is (E-1, ?) with
 156sum 17, forcing ? = 17 - 11 = 6 = F. Then the fourth value must satisfy
 1576 + d = span_down, with span_down = 55 - 24 - 17 = 14, so d = 8 = V.
 158
 159Under this filter, the chain (E+1, E-1, F, V) = (13, 11, 6, 8) is unique.
 160-/
 161
 162/-- If the chain contains both E+1 and E-1 as adjacent values, the chain is
 163    uniquely determined. -/

depends on (33)

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