BT000D

succ_injective

Stable checked-use theorem · independently kernel verified

Successor is injective (the reusable PA2 lemma).

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 n m. S n = S m -> n = m

Structural proof guide

Successor is injective (the reusable PA2 lemma).

Direct prerequisites: none. The authored body proceeds by direct introduction and elimination.

Proof neighborhood

Direct dependencies

none

Direct dependents

BT00TA beta_pascal_row_step_pointwise_functional BT00TB beta_pascal_table_row_pointwise_functional BT00TF beta_pascal_table_diagonal_boundary BT00TH beta_pascal_table_successor_cell_recurrence

Formal native tactic body

Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing Stable membership.

Read the argument

Proof checkpoints

1 script commands · 1 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.

01Use earlier factsL1–1

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L1
    apply PA2

Library-wide reading audit

Original exact command ledger · 1 lines
  1. 0001apply PA2