Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 350 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.31.0

Map Union union map Union

List.mapUnion_union_mapUnion'

Plain-language statement

mapUnion_union_mapUnion applies when you have the same function f and different input lists. mapUnion_union_mapUnion' applies when you have different functions f/g and the same input list.

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

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Project-declaredLean 4.32.0

Map construction

map_construction

Plain-language statement

The T-transform is natural in any oracle-semantics morphism that preserves both the plaintext-to-coins query capability and the distinguished lift of ProbComp.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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Project-declaredLean 4.32.0

Completeness

MerkleTree.completeness

Project documentation

Completeness theorem for Merkle trees: for any full binary tree with 2 ^ n leaves, and for any index i, the honestly-generated opening proof verifies against the honestly-built root with probability one.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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Project-declaredLean 4.32.0

Functional completeness

MerkleTree.functional_completeness

Project documentation

A functional completeness theorem for Merkle proofs built from buildMerkleTree_with_hash.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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Project-declaredLean 4.32.0

Negligible polynomial mul

negligible_polynomial_mul

Project documentation

If f is negligible, then fun n => ↑(p.eval n) * f n is negligible for any polynomial p. This is the key lemma for handling polynomial-loss security reductions.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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Project-declaredLean 4.32.0

Of Real tv Dist bind left le const

ofReal_tvDist_bind_left_le_const

Plain-language statement

ℝ≥0∞ form of tvDist_bind_left_le_const, matching the quantitative APIs: a per-a bound ENNReal.ofReal (tvDist (f a) (g a)) ≤ ε on the support of mx lifts through the shared bind.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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