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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 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 1,591 to 1,596 of 2,569 results.

Project-declaredLean 4.31.0

Map M implies forall₂

List.mapM_implies_forall₂

Mathematical statement

Introduces forall₂ through the input output relation of a f through List.mapM. This is slightly stronger than the forward direction of mapM_ok_iff_forall₂ since it allowed an extra x ∈ xs condition in h.

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

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Project-declaredLean 4.31.0

Map M' error implies exists error

List.mapM'_error_implies_exists_error

Mathematical statement

The converse is not true: counterexample xs is [1, 2] and f is Except.error. In that case, f 2 = .error 2 but xs.mapM' f = .error 1. But for a limited converse, see element_error_implies_mapM_error

authorizationprogram verificationsemantics

Source project: Cedar Specification

Person-level attribution pending.

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Project-declaredLean 4.31.0

Map Union union map Union

List.mapUnion_union_mapUnion'

Mathematical 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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