EU000F

euler_unit_product_factor_unit_value

Public research checkpoint, not admitted to Alpha or Stable. Alpha v30 remains 3222 checked-use theorems; Stable remains 432. The on-demand Alpha Lean service does not yet expose these checkpoint theorems; their independently checked literal bundles and unchanged sources are available below.

Public research checkpoint: original HA and independently compiled Lean verified; not Alpha-enrolled, no Alpha checked-use authority; not Stable

At a genuine unit index the weighted factor is the index itself.

Exact expanded first-order arithmetic statement

forall m i v. (forall eut_divisor_eu_factor_unit. (exists eut_left_eu_factor_unit. (i) = eut_divisor_eu_factor_unit * eut_left_eu_factor_unit) -> (exists eut_right_eu_factor_unit. (m) = eut_divisor_eu_factor_unit * eut_right_eu_factor_unit) -> eut_divisor_eu_factor_unit = 1) -> ((((forall eut_divisor_eu_factor_unit_coprime. (exists eut_left_eu_factor_unit_coprime. (i) = eut_divisor_eu_factor_unit_coprime * eut_left_eu_factor_unit_coprime) -> (exists eut_right_eu_factor_unit_coprime. (m) = eut_divisor_eu_factor_unit_coprime * eut_right_eu_factor_unit_coprime) -> eut_divisor_eu_factor_unit_coprime = 1) /\ (v)=(i)) \/ (~(forall eut_divisor_eu_factor_unit_coprime. (exists eut_left_eu_factor_unit_coprime. (i) = eut_divisor_eu_factor_unit_coprime * eut_left_eu_factor_unit_coprime) -> (exists eut_right_eu_factor_unit_coprime. (m) = eut_divisor_eu_factor_unit_coprime * eut_right_eu_factor_unit_coprime) -> eut_divisor_eu_factor_unit_coprime = 1) /\ (v)=1))) -> v=i

Constructive proof overview

Generated structural guide

At a genuine unit index the weighted factor is the index itself.

The unchanged tactic script uses 0 declared prerequisites and contains 12 exact native proof lines.

Public research checkpoint: original HA and independently compiled Lean verified; not Alpha-enrolled, no Alpha checked-use authority; not Stable

Proof neighborhood

Direct dependencies

none

Direct dependents

EU0018 euler_unit_factor_scaled_congruence

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. The literal dependency-closed bundle is checked by original HA and the independently compiled Lean verifier. Public delivery grants no Alpha checked-use authority or Stable membership.

Read the argument

Proof checkpoints

12 script commands · 5 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.

01Fix variables and assumptionsL1–5

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro m
  2. L2
    intro i
  3. L3
    intro v
  4. L4
    intro hc
  5. L5
    intro hf
02Separate the logical casesL6–7

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L6
    cases hf
  2. L7
    cases hf_left
03Use earlier factsL8–8

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

  1. L8
    exact hf_left_right
04Separate the logical casesL9–10

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L9
    cases hf_right
  2. L10
    exfalso
05Use earlier factsL11–12

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

  1. L11
    apply hf_right_left
  2. L12
    exact hc

Library-wide reading audit

Original exact command ledger · 12 lines
  1. 0001intro m
  2. 0002intro i
  3. 0003intro v
  4. 0004intro hc
  5. 0005intro hf
  6. 0006cases hf
  7. 0007cases hf_left
  8. 0008exact hf_left_right
  9. 0009cases hf_right
  10. 0010exfalso
  11. 0011apply hf_right_left
  12. 0012exact hc