tetragonal_fold_from_8
plain-language theorem explainer
The equality 8/2 = 4 encodes the 4-fold rotational axis that defines the tetragonal crystal system in the Recognition Science derivation of crystallographic symmetries. Workers enumerating the seven crystal systems from the 8-tick octave and space-filling constraints would cite this arithmetic step. The proof is a direct reflexivity reduction on the integer division.
Claim. $8/2 = 4$ supplies the 4-fold axis required for the tetragonal crystal system.
background
The module derives crystal symmetry from the 8-tick octave (period 2^3) that forces three spatial dimensions. Periodic filling of 3D space then restricts rotations to orders 1, 2, 3, 4, and 6; 5-fold and 7-fold axes are excluded because they cannot tile space without gaps. Tetragonal systems are characterized by a single 4-fold axis, which the present equality isolates from the underlying 8-tick ledger.
proof idea
The proof is a one-line wrapper that applies the reflexivity tactic to the arithmetic identity 8/2 = 4.
why it matters
This step supplies the explicit arithmetic link for the tetragonal entry in the seven crystal systems listed in the module documentation. It follows directly from the 8-tick structure (T7) and the space-filling constraint that yields exactly the allowed rotation orders 1, 2, 3, 4, 6. The declaration closes one concrete case in the enumeration of point groups and Bravais lattices.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.