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.
Statement with defined notation
∀ b. ∀ c. InjectivePrefix(b,c,0)Every purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall b c. (forall wpo_injective_left_wpoi_zero_injective wpo_injective_right_wpoi_zero_injective wpo_injective_value_wpoi_zero_injective. (exists wpo_gap_wpoi_zero_injective_left_bound. wpo_gap_wpoi_zero_injective_left_bound + S (wpo_injective_left_wpoi_zero_injective) = 0) -> (exists wpo_gap_wpoi_zero_injective_right_bound. wpo_gap_wpoi_zero_injective_right_bound + S (wpo_injective_right_wpoi_zero_injective) = 0) -> (((exists wpo_beta_height_wpoi_zero_injective_left_entry. wpo_beta_height_wpoi_zero_injective_left_entry + S (wpo_injective_value_wpoi_zero_injective) = S ((S (wpo_injective_left_wpoi_zero_injective)) * c)) /\ exists wpo_beta_quotient_wpoi_zero_injective_left_entry. b = wpo_beta_quotient_wpoi_zero_injective_left_entry * S ((S (wpo_injective_left_wpoi_zero_injective)) * c) + (wpo_injective_value_wpoi_zero_injective))) -> (((exists wpo_beta_height_wpoi_zero_injective_right_entry. wpo_beta_height_wpoi_zero_injective_right_entry + S (wpo_injective_value_wpoi_zero_injective) = S ((S (wpo_injective_right_wpoi_zero_injective)) * c)) /\ exists wpo_beta_quotient_wpoi_zero_injective_right_entry. b = wpo_beta_quotient_wpoi_zero_injective_right_entry * S ((S (wpo_injective_right_wpoi_zero_injective)) * c) + (wpo_injective_value_wpoi_zero_injective))) -> wpo_injective_left_wpoi_zero_injective = wpo_injective_right_wpoi_zero_injective)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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 (2)
01Fix variables and assumptionsL1–9
02Separate the logical casesL10–11
03Establish hsqL12–19
Establish this local claim before using it. It is not an additional assumption. The following proof commands apply add eq zero right.
Original defined command ledger · 19 lines
- 0001
intro b - 0002
intro c - 0003
intro q - 0004
intro r - 0005
intro w - 0006
intro hq - 0007
intro hr - 0008
intro hleft - 0009
intro hright - 0010
exfalso - 0011
cases hq - 0012
have hsq : S q = 0 - 0013
specialize add_eq_zero_right x - 0014
specialize add_eq_zero_right (S q) - 0015
apply add_eq_zero_right - 0016
exact hq_witness - 0017
specialize succ_ne_zero q - 0018
apply succ_ne_zero - 0019
exact hsq