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 a c x. (((a) = (c) + (x) \/ (c) = (a) + (x))) -> x = 0 -> a = cEvery purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.
Definitions used by this theorem
In the theorem statement
In local proof propositions
Exact expanded first-order statement
forall a c x. (((a) = (c) + (x) \/ (c) = (a) + (x))) -> x = 0 -> a = cProof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay 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.
01Fix variables and assumptionsL1–5
02Separate the logical casesL6–6
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L6
cases hdifference
03Calculate and transport equalitiesL7–8
04Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
exact hdifference_left
05Calculate and transport equalitiesL10–13
06Use earlier factsL14–14
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L14
exact hdifference_right
07Calculate and transport equalitiesL15–15
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L15
simp