Succ Succ Above comm
Fin.succSuccAbove_comm
Project documentation
The preimage of m under succSuccAbove i j hij given that m is not equal to i or j. -/ def predPredAbove (i j : Fin (n + 1 + 1)) (hij : i ≠ j) (m : Fin (n + 1 + 1)) (hm : m ≠ i ∧ m ≠ j) : Fin n := if h1 : m.1 < i.1 ∧ m.1 < j.1 then ⟨m, by grind⟩ else if h2 : m.1 - 1 < i.1 ∧ j.1 ≤ m.1 then ⟨m - 1, by grind⟩ else if h3 : i.1 - 1 ≤ m.1 ∧ m.1 < j.1 t...
Exact Lean statement
lemma succSuccAbove_comm (i1 j1 : Fin (n + 1 + 1 + 1 + 1)) (i2 j2 : Fin (n + 1 + 1))
(hij1 : i1 ≠ j1) (hij2 : i2 ≠ j2) :
let i2'Formal artifact
Lean source
lemma succSuccAbove_comm (i1 j1 : Fin (n + 1 + 1 + 1 + 1)) (i2 j2 : Fin (n + 1 + 1)) (hij1 : i1 ≠ j1) (hij2 : i2 ≠ j2) : let i2' := (succSuccAbove i1 j1 i2); let j2' := (succSuccAbove i1 j1 j2); have hi2j2' : i2' ≠ j2' := by simp [i2', j2', hij2]; let i1' := (predPredAbove i2' j2' hi2j2' i1 (by simp [i2', j2'])); let j1' := (predPredAbove i2' j2' hi2j2' j1 (by simp [i2', j2'])); succSuccAbove i1 j1 ∘ succSuccAbove i2 j2 = succSuccAbove i2' j2' ∘ succSuccAbove i1' j1':= by ext m simp only [Function.comp_apply, predPredAbove_val, succSuccAbove_val] grind (splits := 20)- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Tensors/Contraction/SuccSuccAbove.lean:324-335
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.