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

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Project-declaredLean 4.8.0

Exp congr

Prob.exp_congr'

Plain-language statement

General congruence for exp, allowing the probabilities to be different

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Exp eq cexp add cexp

Prob.exp_eq_cexp_add_cexp

Plain-language statement

exp can be decomposed as positive and negative cexps, even if there are zeros

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Exp eq exp cexp

Prob.exp_eq_exp_cexp

Plain-language statement

exp can be decomposed as a expectation over cexp's w.r.t. a function

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Exp eq zero iff

Prob.exp_eq_zero_iff

Plain-language statement

f.exp u = 0 in terms of forall, for nonnegative u

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Exp le exp of map

Prob.exp_le_exp_of_map

Plain-language statement

Bound one exp in terms of another on a different space by injecting between the spaces

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Exp mono

Prob.exp_mono'

Plain-language statement

Expectation is monotonic, general version for different distributions

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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