EU000F

euler_unit_product_factor_unit_value

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

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

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 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.

Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; 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. 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

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