Left size $1$ , right size $6$ : no such EML tree evaluates to $2$

Proved

EmlComplexity.not_attains_two_pair_1_6

by WillR · Sep 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

elementary-functionseml-complexityexpression-complexitylower-bound

Finite check over a fixed-shape family of closed EML trees (total size $8$ ): no valid instance evaluates to $2$ , by certified enclosures with exact degenerate handling. One group of the size- $8$ lower-bound band.

Preamble

import Definitions.Def_EmlComplexity

Formal statement

namespace EmlComplexity
theorem not_attains_two_pair_1_6 : ∀ a b : Tree, a.size = 1 → b.size = 6 → Tree.valid (Tree.node a b) → Tree.eval (Tree.node a b) ≠ 2 := by sorry
end EmlComplexity

Source

Odrzywolek, All elementary functions from a single operator, arXiv:2603.21852 (2026), Section 4.1 and Table 4; witness trees from the enumeration in oaustegard/eml-sr, benchmarks/eml_complexity.md (2026-09-04)

View graph

Left size 111, right size 666: no such EML tree evaluates to 222

Left size $1$ , right size $6$ : no such EML tree evaluates to $2$