MATHLIBANNEX / PROJECT LFH

Reflection and midpoint rigidity

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Scope

A bounded symmetric lens and reflection-center rigidity identify midpoints under an isometry. Containment in matching ambient balls supplies the local hypotheses for midpoint preservation.

5 direct Cards + 0 reused prerequisites = 5 unique Cards. This count is a selected Card closure, not a source-declaration count.

Route reading PDF · Preserved source exploration

Cards in this route

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Reference index: direct Cards and reused prerequisites

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

Reused prerequisites: None in this scope.

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.

5 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

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Level 1 (1 Card)

Level 2 (1 Card)

Level 3 (1 Card)