PA006T — odd_half

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 a b. n = 2 * a + 1 -> n = 2 * b + 1 -> a = b

Structural proof guide

Generated structural guide

The half witness in an odd decomposition is unique.

Use the direct prerequisites add_right_cancel, mul_left_cancel_nonzero as previously established PA formulas.

The proof proceeds by intermediate claims (2).

Referenced ingredients

PA0012 add_right_cancel PA006S mul_left_cancel_nonzero

Proof neighborhood

Direct dependencies

PA0012 add_right_cancel PA006S mul_left_cancel_nonzero

Direct dependents

PA00FI odd_half_of_mod4_one_exact PA00FQ odd_half_of_mod4_three_exact

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

24 script commands · 5 reading checkpoints · 2 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.

Named ingredients (2)

add right cancel mul left cancel nonzero

01Fix variables and assumptionsL1–5

Work with arbitrary variables or the premises of the current implication.