Research proof index

Fin.induction on m + n for m + i steps is equivalent to Fin.induction on n on i steps on the result of Fin.induction on m.

The conservative and convective Euler forms are equivalent when the fields are differentiable enough for the product rules.

Two almost-everywhere strongly measurable functions on the circle that agree almost everywhere have the same Fourier coefficient at every fixed integer frequency $n$.

The q-adic valuation of the j-invariant of the Frey curve is a multiple of p if 2 < q is a prime of bad reduction.

A version of fundamental_theorem_of_variational_calculus' for Continuous f. The proof uses assumption that source of f is finite-dimensional inner-product space, so that a bump function with compact support exists via ContDiffBump.hasCompactSupport from Analysis.Calculus.BumpFunction.Basic. The proof is by contradiction, assume that there is `x₀...

A version of fundamental_theorem_of_variational_calculus' for Continuous f. The proof uses assumption that source of f is finite-dimensional inner-product space, so that a bump function with compact support exists via ContDiffBump.hasCompactSupport from Analysis.Calculus.BumpFunction.Basic. The proof is by contradiction, assume that there is `x₀...