Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 591 research declarations. Search 10,000 more complete Mathlib declarations.

All topics

591 results

Clear filters
Project-declaredLean 4.32.0

VAbs sum sq row eq one

CKMMatrix.VAbs_sum_sq_row_eq_one

Plain-language statement

The absolute value squared of any row of a CKM matrix is 1, in terms of Vabs.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Acceleration eq of equation Of Motion

ClassicalMechanics.DampedHarmonicOscillator.acceleration_eq_of_equationOfMotion

Plain-language statement

Solving the equation of motion for the acceleration: along a solution the second derivative is -(k/m) x - (γ/m) ẋ.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Equation Of Motion unique

ClassicalMechanics.DampedHarmonicOscillator.equationOfMotion_unique

Plain-language statement

Any two smooth solutions of the damped equation of motion with the same initial position and velocity are equal.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Grad Lagrangian eq force

ClassicalMechanics.DampedHarmonicOscillator.gradLagrangian_eq_force

Plain-language statement

The variational gradient of the Caldirola–Kanai action is the exponential factor times the difference of the force and mass times acceleration appearing in Newton's second law.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

To Undamped equation Of Motion

ClassicalMechanics.DampedHarmonicOscillator.toUndamped_equationOfMotion

Plain-language statement

When γ = 0, the damped equation of motion is equivalent to the equation of motion for the corresponding undamped harmonic oscillator.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Trajectory equation Of Motion of critically Damped

ClassicalMechanics.DampedHarmonicOscillator.trajectory_equationOfMotion_of_criticallyDamped

Plain-language statement

In the critically damped regime, the selected trajectory satisfies the damped equation of motion.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record