# Supplied prerequisite proofs

Each result used by a lesson has its proof locally or in an exact supplied earlier programme reading. Bibliographical references support construction and do not replace these proofs.

- [Complex smooth division of order one](prerequisites/U011-free-foundations/AN04-order-one-division.html) · [editable source](prerequisites/U011-free-foundations/AN04-order-one-division.md) · CC0-1.0
- [Angular tests, point jets and polar integration](prerequisites/U011-free-foundations/angular-foundations-U018.html) · [editable source](prerequisites/U011-free-foundations/angular-foundations-U018.md) · CC0-1.0
- [Lebesgue integration and smoothing — selected programme proofs](prerequisites/U011-free-foundations/banach-foundation-bridges.html) · [editable source](prerequisites/U011-free-foundations/banach-foundation-bridges.md) · CC0 1.0
- [Cauchy integrals, zeros and contour indices](prerequisites/U011-free-foundations/complex-contours-U070.html) · [editable source](prerequisites/U011-free-foundations/complex-contours-U070.md) · CC0 1.0
- [Functional extension and complete test spaces](prerequisites/U011-free-foundations/functional-foundations-U008.html) · [editable source](prerequisites/U011-free-foundations/functional-foundations-U008.md) · CC0 1.0
- [The gamma integral and its entire reciprocal](prerequisites/U011-free-foundations/gamma-foundations-U016.html) · [editable source](prerequisites/U011-free-foundations/gamma-foundations-U016.md) · CC0 1.0
- [Smooth inverse and implicit maps](prerequisites/U011-free-foundations/implicit-maps-U070.html) · [editable source](prerequisites/U011-free-foundations/implicit-maps-U070.md) · CC0 1.0
- [Scalar calculus and Euclidean topology — selected programme proofs](prerequisites/U011-free-foundations/metric-foundation-bridges.html) · [editable source](prerequisites/U011-free-foundations/metric-foundation-bridges.md) · CC0 1.0
- [Polynomial division and all complex roots](prerequisites/U011-free-foundations/polynomial-roots-U070.html) · [editable source](prerequisites/U011-free-foundations/polynomial-roots-U070.md) · CC0 1.0
- [Positive functionals and locally finite measures](prerequisites/U011-free-foundations/positive-measure-foundations-U008.html) · [editable source](prerequisites/U011-free-foundations/positive-measure-foundations-U008.md) · CC0-1.0
- [Schwartz functions and Fourier inversion](prerequisites/U011-free-foundations/schwartz-fourier-foundations-U017.html) · [editable source](prerequisites/U011-free-foundations/schwartz-fourier-foundations-U017.md) · CC0-1.0
- [Smooth flows with all parameter derivatives](prerequisites/U011-free-foundations/smooth-parameter-flows-U072.html) · [editable source](prerequisites/U011-free-foundations/smooth-parameter-flows-U072.md) · CC0 1.0
- [Complex scalars and finite algebra — selected programme proofs](prerequisites/U011-free-foundations/stable-prerequisite-bridges.html) · [editable source](prerequisites/U011-free-foundations/stable-prerequisite-bridges.md) · CC0 1.0
- [Weierstrass preparation and division](prerequisites/U011-free-foundations/weierstrass-preparation-U070.html) · [editable source](prerequisites/U011-free-foundations/weierstrass-preparation-U070.md) · CC0 1.0

[The HA-LCA quotient/lattice route](prerequisites/HA-LCA-724d1a8/AN01-INTEGRATION.html) includes its complete provider edition and precise record of the 192 proof blocks checked for AN-01.

- [Smooth pullback and the Fourier normal condition](reader/AN01-U083-prerequisite.html): complete AN-03 Sections18.1–18.5, with the programme foundation proofs used for noncharacteristic pullback, coordinate changes and submersions. CC0.

- [Supporting quadratics and nearest-point normals](reader/AN01-U085-prerequisite.html): complete geometric arguments from AN-03 Sections1 and7 on strict quadratic support and nearest-point normals, with their programme calculus proofs. CC0.

- [Contour identity for holomorphic approximation](prerequisites/U011-free-foundations/contour-homotopy-U095.html): exact AN-04 Section A2 identity, determinant proof and cutoff discussion. CC0.

- [Smooth parameter slices from the normal condition](reader/AN01-U101-prerequisite.html): complete AN-03 Section18.6, identifying the actual strong smooth distribution family and its normal restrictions, with all preceding proofs supplied. CC0.

- [Disk comparison and Poisson integrals](prerequisites/U011-free-foundations/AN04-disk-comparison-U129.html): AN-04 P1, harmonic comparison, circle means and the Poisson formula.

- [A matrix estimate with a semipositive imaginary part](prerequisites/U011-free-foundations/AN04-positive-matrix-U130.html): complete selected AN-04 mathematical arguments and their earlier proof links.

- [Contour calculus and the Gaussian branch](prerequisites/U011-free-foundations/AN04-contour-calculus-U130.html): complete selected AN-04 mathematical arguments and their earlier proof links.

- [Gaussian reduction near a complex critical graph](prerequisites/U011-free-foundations/AN04-complex-contours-U130.html): complete selected AN-04 mathematical arguments and their earlier proof links.

- [Flow inverses and continuation on their actual domains](prerequisites/U011-free-foundations/flow-inverses-and-continuation-U134.html): complete selected programme arguments and their earlier proof links.

- [Smooth quadratic coordinates and their Jacobian](prerequisites/U011-free-foundations/AN04-parameter-morse-U134.html): complete selected programme arguments and their earlier proof links.

- [Operator completeness and open mapping](prerequisites/U011-free-foundations/operator-completeness-and-open-mapping.html) · [editable source](prerequisites/U011-free-foundations/operator-completeness-and-open-mapping.md) · CC0-1.0

- [Real spectral decomposition](prerequisites/U011-free-foundations/real-spectral-decomposition.html) · [editable source](prerequisites/U011-free-foundations/real-spectral-decomposition.md) · CC0-1.0