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 a u c r s. r = a * c + s -> a * u + r = a * (u + c) + sStructural proof guide
Generated structural guide
Absorb a second quotient into an existing residue equation.
Use the direct prerequisites add_assoc, mul_add as previously established PA formulas.
The proof proceeds by direct introduction and elimination.
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
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
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 assumptionsL1–6
02Calculate and transport equalitiesL7–9
03Use earlier factsL10–10
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L10
exact hr
04Calculate and transport equalitiesL11–12
05Use earlier factsL13–13
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L13
apply add_assoc
06Calculate and transport equalitiesL14–15
07Use earlier factsL16–16
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L16
apply mul_add
08Calculate and transport equalitiesL17–17
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L17
refl