PA006T — odd_half_unique — defined notation

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

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

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

none

0 occurrences

In local proof propositions

none

0 occurrences

Exact expanded native-PA statement

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

Proof neighborhood

Direct theorem prerequisites

PA0012 add_right_cancel PA006S mul_left_cancel_nonzero

Direct theorem dependents

PA00FI odd_half_of_mod4_one_exact PA00FQ odd_half_of_mod4_three_exact

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

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.

Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.

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.