Energy Mass is Dimensionally Correct
UnitExamples.energyMass_isDimensionallyCorrect
Project documentation
The lemma that the proposition EnergyMass is dimensionally correct
Exact Lean statement
lemma energyMass_isDimensionallyCorrect :
IsDimensionallyCorrect EnergyMassFormal artifact
Lean source
lemma energyMass_isDimensionallyCorrect : IsDimensionallyCorrect EnergyMass := by /- Scale such that the unit u1 is taken to u2. -/ intro u1 u2 /- Let `m` be the mass, `E` be the energy and `u` be the actual units we start with. -/ funext m E u unfold EnergyMass simp only [eq_iff_iff, UnitDependent.scaleUnit_apply_fun_left, UnitDependent.scaleUnit_apply_fun, Dimensionful.of_scaleUnit, dim_apply, WithDim.scaleUnit_val, WithDim.smul_val, map_mul, mul_pow, NNReal.smul_def, smul_eq_mul, NNReal.coe_mul] ring_nf simp [mul_assoc, mul_eq_mul_left_iff, dimScale_ne_zero]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Units/Examples.lean:144-156
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
Related declarations
Adiabatic relation log
adiabatic_relation_log
Plain-language statement
Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.
Source project: Physlib
Person-level attribution pending.
Adiabatic relation Ua Ub Va Vb
adiabatic_relation_UaUbVaVb
Plain-language statement
Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.
Source project: Physlib
Person-level attribution pending.
Deriv Within mean Energy Beta eq neg variance
CanonicalEnsemble.derivWithin_meanEnergy_Beta_eq_neg_variance
Plain-language statement
(∂U/∂β) = -Var(E) for finite systems.
Source project: Physlib
Person-level attribution pending.