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 PA statement
forall b c z d a l. (forall ff_i_transport_l. (exists ff_lt_transport_l_bound. ff_lt_transport_l_bound + S ff_i_transport_l = l) -> (((exists ff_h_transport_l_decoded. ff_h_transport_l_decoded + S (a) = S ((S (ff_i_transport_l)) * c)) /\ exists ff_q_transport_l_decoded. b = ff_q_transport_l_decoded * S ((S (ff_i_transport_l)) * c) + (a)))) -> (forall ff_i_transport_r. (exists ff_lt_transport_r_bound. ff_lt_transport_r_bound + S ff_i_transport_r = l) -> (((exists ff_h_transport_r_decoded. ff_h_transport_r_decoded + S (a) = S ((S (ff_i_transport_r)) * d)) /\ exists ff_q_transport_r_decoded. z = ff_q_transport_r_decoded * S ((S (ff_i_transport_r)) * d) + (a)))) -> forall i x. (exists h. h + S i = l) -> (((exists ff_h_transport_x. ff_h_transport_x + S (x) = S ((S (i)) * c)) /\ exists ff_q_transport_x. b = ff_q_transport_x * S ((S (i)) * c) + (x))) -> (((exists ff_h_transport_y. ff_h_transport_y + S (x) = S ((S (i)) * d)) /\ exists ff_q_transport_y. z = ff_q_transport_y * S ((S (i)) * d) + (x)))Structural proof guide
Generated structural guide
Repeat prefixes with one value preserve every decoded entry extensionally.
Use the direct prerequisites beta_repeat_entry_eq as previously established PA formulas.
The proof proceeds by intermediate claims (1), equality transport (2).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.
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 assumptionsL1–10
02Fix variables and assumptionsL11–12
03Establish hxaL13–22
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply beta repeat entry eq.
04Use earlier factsL23–23
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L23
exact hx
05Calculate and transport equalitiesL24–25
Original exact command ledger · 28 lines
- 0001
intro b - 0002
intro c - 0003
intro z - 0004
intro d - 0005
intro a - 0006
intro l - 0007
intro hleft - 0008
intro hright - 0009
intro i - 0010
intro x - 0011
intro hi - 0012
intro hx - 0013
have hxa : x = a - 0014
specialize beta_repeat_entry_eq b - 0015
specialize beta_repeat_entry_eq c - 0016
specialize beta_repeat_entry_eq a - 0017
specialize beta_repeat_entry_eq l - 0018
specialize beta_repeat_entry_eq i - 0019
specialize beta_repeat_entry_eq x - 0020
apply beta_repeat_entry_eq - 0021
exact hleft - 0022
exact hi - 0023
exact hx - 0024
rewrite hxa - 0025
rewrite hxa - 0026
specialize hright i - 0027
apply hright - 0028
exact hi