95 new Alpha admissions come from 96 source lemmas: tuple equality reflexivity reuses an already-admitted theorem and is not counted twice. All counts use actual finite beta-coded enumerations. G008 multiplicativity is proved; the general prime-power count and distinct-prime product formula are further goals. General prime-power fields (G091) remain open. Stable is unchanged.
Exact theorem in conservative defined notation
∀ k. ∀ n. ∀ u. ∀ v. JordanTotient(k,n,u) → JordanTotient(k,n,v) → u = v
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 33 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.
Read the argument
Proof checkpoints
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 (1)
01Fix variables and assumptionsL1–6
02Separate the logical casesL7–16
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
03Separate the logical casesL17–18
04Use earlier factsL19–28
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L19
specialize jordan_enumeration_cardinality_unique (k) - L20
specialize jordan_enumeration_cardinality_unique (n) - L21
specialize jordan_enumeration_cardinality_unique (x) - L22
specialize jordan_enumeration_cardinality_unique (x1) - L23
specialize jordan_enumeration_cardinality_unique (x2) - L24
specialize jordan_enumeration_cardinality_unique (x3) - L25
specialize jordan_enumeration_cardinality_unique (u) - L26
specialize jordan_enumeration_cardinality_unique (x4) - L27
specialize jordan_enumeration_cardinality_unique (x5) - L28
specialize jordan_enumeration_cardinality_unique (x6)
05Use earlier factsL29–33
Instantiate or apply named facts and discharge the corresponding proof obligations.
Original defined command ledger · 33 lines
- 0001
intro k - 0002
intro n - 0003
intro u - 0004
intro v - 0005
intro hl - 0006
intro hr - 0007
cases hl - 0008
cases hl_right - 0009
cases hr - 0010
cases hr_right - 0011
cases hl_right_right - 0012
cases hl_right_right_witness - 0013
cases hl_right_right_witness_witness - 0014
cases hl_right_right_witness_witness_witness - 0015
cases hr_right_right - 0016
cases hr_right_right_witness - 0017
cases hr_right_right_witness_witness - 0018
cases hr_right_right_witness_witness_witness - 0019
specialize jordan_enumeration_cardinality_unique (k) - 0020
specialize jordan_enumeration_cardinality_unique (n) - 0021
specialize jordan_enumeration_cardinality_unique (x) - 0022
specialize jordan_enumeration_cardinality_unique (x1) - 0023
specialize jordan_enumeration_cardinality_unique (x2) - 0024
specialize jordan_enumeration_cardinality_unique (x3) - 0025
specialize jordan_enumeration_cardinality_unique (u) - 0026
specialize jordan_enumeration_cardinality_unique (x4) - 0027
specialize jordan_enumeration_cardinality_unique (x5) - 0028
specialize jordan_enumeration_cardinality_unique (x6) - 0029
specialize jordan_enumeration_cardinality_unique (x7) - 0030
specialize jordan_enumeration_cardinality_unique (v) - 0031
apply jordan_enumeration_cardinality_unique - 0032
exact hl_right_right_witness_witness_witness_witness - 0033
exact hr_right_right_witness_witness_witness_witness