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. ∀ c. ∀ t. ∀ B. ∀ C. ∀ D. ∀ E. ∀ j. JordanTupleScan(k,n,c,t,B,C,D,E,j) → (BetaPrefixInto(t,c,k,n) → JordanPrimitiveTuple(n,t,c,k) → JordanTupleListed(t,c,k,B,C,D,E,j)) → JordanTupleScan(k,n,c,S t,B,C,D,E,j)
Every linked abbreviation expands hygienically to the identical original native formula.
Definition DAG
Actual proof prerequisites
Complete tactic proof in conservative notation
All 38 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.
01Fix variables and assumptionsL1–10
02Fix variables and assumptionsL11–11
Work with arbitrary variables or the premises of the current implication.
- L11
intro hcurrent
03Separate the logical casesL12–14
04Use earlier factsL15–15
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L15
exact hscan_left
05Separate the logical casesL16–16
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L16
split
06Use earlier factsL17–17
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L17
exact hscan_right_left
07Fix variables and assumptionsL18–21
08Establish hcL22–26
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply finite lt succ eq or lt.
09Separate the logical casesL27–27
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L27
cases hc
10Calculate and transport equalitiesL28–28
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L28
rewrite hc_left
11Use earlier factsL29–29
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L29
apply hcurrent
12Calculate and transport equalitiesL30–30
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L30
rewrite hc_left at hb
13Use earlier factsL31–31
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L31
exact hb
14Calculate and transport equalitiesL32–32
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L32
rewrite hc_left at hp
Original defined command ledger · 38 lines
- 0001
intro k - 0002
intro n - 0003
intro c - 0004
intro t - 0005
intro B - 0006
intro C - 0007
intro D - 0008
intro E - 0009
intro j - 0010
intro hscan - 0011
intro hcurrent - 0012
cases hscan - 0013
cases hscan_right - 0014
split - 0015
exact hscan_left - 0016
split - 0017
exact hscan_right_left - 0018
intro z - 0019
intro hz - 0020
intro hb - 0021
intro hp - 0022
have hc : z = t ∨ Lt(z,t) - 0023
specialize finite_lt_succ_eq_or_lt (t) - 0024
specialize finite_lt_succ_eq_or_lt (z) - 0025
apply finite_lt_succ_eq_or_lt - 0026
exact hz - 0027
cases hc - 0028
rewrite hc_left - 0029
apply hcurrent - 0030
rewrite hc_left at hb - 0031
exact hb - 0032
rewrite hc_left at hp - 0033
exact hp - 0034
specialize hscan_right_right (z) - 0035
apply hscan_right_right - 0036
exact hc_right - 0037
exact hb - 0038
exact hp