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 573 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.31.0

Indicator eq 1 of neg empty empty of pos nonempty

Polynomial.indicator_eq_1_of_neg_empty_empty_of_pos_nonempty

Plain-language statement

The indicator polynomial is a constant one polynomial if the set neg is empty while pos is not.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Indicator eq 1 on pos

Polynomial.indicator_eq_1_on_pos

Plain-language statement

Indicator evaluated on an element of pos is equal to 1.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Indicator ne zero of pos nonempty

Polynomial.indicator_ne_zero_of_pos_nonempty

Plain-language statement

If pos is non-empty then the indicator polynomial is the constant zero polynomial.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Split Nth of sum comp

Polynomial.splitNth_of_sum_comp

Plain-language statement

splitNth is the left inverse of the n-way recombination: splitting the polynomial ∑ j, X^j * (u j)(X^n) recovers u i for each component i.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Poly gen is zero evading

PolynomialGenerator.poly_gen_is_zero_evading

Plain-language statement

If G is a polynomial generator, then G is zero-evading with error the maximum of the total degrees of the individual polynomials divided by the size of the smallest evaluation sets S i. Remark 3.20, the version of the statement in the brackets [BCGM25]. Note: Remark 3.20 provides two ways of viewing a polynomial generator as a zero-evading generator...

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Pr add split by complement

Pr_add_split_by_complement

Plain-language statement

Law of Total Probability (Partitioning an Event) The probability of an event f r occurring can be calculated by summing the probabilities of two disjoint cases: 1. f r occurs AND g r occurs. 2. f r occurs AND g r does NOT occur. Good to be used with Pr_multi_let_equiv_single_let

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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