GF000E

gaussian_one_representation

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

The actual canonical Gaussian one code is 6, with its signed coordinates proved rather than asserted.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Exact expanded first-order arithmetic statement

exists ge_representation_real_code_ring_one_representation ge_representation_imaginary_code_ring_one_representation. (((6) = ((ge_representation_real_code_ring_one_representation) + (ge_representation_imaginary_code_ring_one_representation)) * S ((ge_representation_real_code_ring_one_representation) + (ge_representation_imaginary_code_ring_one_representation)) + ((ge_representation_imaginary_code_ring_one_representation) + (ge_representation_imaginary_code_ring_one_representation))) /\ ((exists ge_balance_positive_ring_one_representationreal ge_balance_negative_ring_one_representationreal. (((((ge_representation_real_code_ring_one_representation) = 2 * (ge_balance_positive_ring_one_representationreal) /\ (ge_balance_negative_ring_one_representationreal) = 0) \/ exists ge_signed_half_ring_one_representationrealdecode. (((ge_representation_real_code_ring_one_representation) = 2 * ge_signed_half_ring_one_representationrealdecode + 1 /\ (ge_balance_positive_ring_one_representationreal) = 0) /\ (ge_balance_negative_ring_one_representationreal) = S ge_signed_half_ring_one_representationrealdecode))) /\ ((1) + ge_balance_negative_ring_one_representationreal = (0) + ge_balance_positive_ring_one_representationreal))) /\ (exists ge_balance_positive_ring_one_representationimaginary ge_balance_negative_ring_one_representationimaginary. (((((ge_representation_imaginary_code_ring_one_representation) = 2 * (ge_balance_positive_ring_one_representationimaginary) /\ (ge_balance_negative_ring_one_representationimaginary) = 0) \/ exists ge_signed_half_ring_one_representationimaginarydecode. (((ge_representation_imaginary_code_ring_one_representation) = 2 * ge_signed_half_ring_one_representationimaginarydecode + 1 /\ (ge_balance_positive_ring_one_representationimaginary) = 0) /\ (ge_balance_negative_ring_one_representationimaginary) = S ge_signed_half_ring_one_representationimaginarydecode))) /\ ((0) + ge_balance_negative_ring_one_representationimaginary = (0) + ge_balance_positive_ring_one_representationimaginary)))))

Constructive proof overview

Generated structural guide

The actual canonical Gaussian one code is 6, with its signed coordinates proved rather than asserted.

The unchanged tactic script uses 2 declared prerequisites and contains 10 exact native proof lines.

Alpha v34 checked-use · first admitted v30 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

GF0002 gaussian_code_representation_transport GF000A gaussian_natural_real_representation

Direct dependents

GF000F gaussian_one_valid GF0010 gaussian_one_norm GF001A gaussian_norm_one_is_unit GF0028 gaussian_multiply_one_right

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

10 script commands · 3 reading checkpoints · 0 local claims

This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.

Named ingredients (2)
gaussian code representation transportgaussian natural real representation
01Use earlier factsL1–7

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L1
    specialize gaussian_code_representation_transport (((2*1) + (0)) * S ((2*1) + (0)) + ((0) + (0)))
  2. L2
    specialize gaussian_code_representation_transport (6)
  3. L3
    specialize gaussian_code_representation_transport (1)
  4. L4
    specialize gaussian_code_representation_transport (0)
  5. L5
    specialize gaussian_code_representation_transport (0)
  6. L6
    specialize gaussian_code_representation_transport (0)
  7. L7
    apply gaussian_code_representation_transport
02Calculate and transport equalitiesL8–8

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L8
    norm_num
03Use earlier factsL9–10

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L9
    specialize gaussian_natural_real_representation (1)
  2. L10
    apply gaussian_natural_real_representation

Library-wide reading audit

Original exact command ledger · 10 lines
  1. 0001specialize gaussian_code_representation_transport (((2*1) + (0)) * S ((2*1) + (0)) + ((0) + (0)))
  2. 0002specialize gaussian_code_representation_transport (6)
  3. 0003specialize gaussian_code_representation_transport (1)
  4. 0004specialize gaussian_code_representation_transport (0)
  5. 0005specialize gaussian_code_representation_transport (0)
  6. 0006specialize gaussian_code_representation_transport (0)
  7. 0007apply gaussian_code_representation_transport
  8. 0008norm_num
  9. 0009specialize gaussian_natural_real_representation (1)
  10. 0010apply gaussian_natural_real_representation