MATHLIBANNEX / PROJECT LFH

Local affine-isometry charts

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Scope

Midpoint preservation yields preservation of affine segments on a smaller ball. The exact source path through omitted radial-map helpers constructs one ambient affine isometry agreeing with the given map there.

2 direct Cards + 5 reused prerequisites = 7 unique Cards. This count is a selected Card closure, not a source-declaration count.

Route reading PDF · Preserved source exploration

Cards in this route

Read this route with prerequisites

Reference index: direct Cards and reused prerequisites

Direct references: M06 — Affine-segment preservation on a quarter ball · M07 — Local affine-isometry chart on a smaller ball

Reused prerequisites: M02 — Center transport under bounded point-reflection symmetry · M03 — Midpoint preservation on a symmetric lens · M01 — Symmetric lens · M05 — Midpoint preservation on a quarter ball · M04 — Midpoint preservation under lens containment

Dependency-first reading route

Read selected Card prerequisites before their uses. Levels are recomputed from the selected reachability-preserving projection; omitted source helpers remain traceable in the source exploration.

7 Cards

Level 0 (2 Cards)

Level 0

Center transport under bounded point-reflection symmetry

Uses a doubling argument to identify the reflection centers under a bijective isometry.

MathlibAnnex.IsometryEquiv.map_center_of_mapsTo_pointReflection

Immediate Card prerequisites: None in this selected scope

Used by in this scope: Midpoint preservation on a symmetric lens

Open Declaration Card Read exact source

Level 1 (1 Card)

Level 2 (1 Card)

Level 3 (1 Card)

Level 4 (1 Card)

Level 5 (1 Card)