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

All topics

150 results

Clear filters
Project-declaredLean 4.32.0

Simulate Q run writer Preserves Inv

OracleComp.simulateQ_run_writerPreservesInv

Plain-language statement

If impl preserves the writer invariant Inv, then simulating any oracle computation with simulateQ impl preserves Inv on the final accumulated writer (support-wise).

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Some Output Satisfies When iff support When

OracleComp.someOutputSatisfiesWhen_iff_supportWhen

Plain-language statement

Some output of oa reachable under possibleOutputs satisfies outputPred exactly when outputPred holds at some point of oa.supportWhen possibleOutputs.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Sq prob Output map le observed Fork Pair

OracleComp.sq_probOutput_map_le_observedForkPair

Plain-language statement

Fixed-index observed success squares under two independent completions of the selected occurrence context.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Support lift Comp

OracleComp.support_liftComp

Plain-language statement

Support is preserved by liftComp: lifting a computation to a larger oracle spec does not change which outputs are reachable. This is the support analogue of evalDist_liftComp.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Support simulate Q run' subset

OracleComp.support_simulateQ_run'_subset

Plain-language statement

Simulating an OracleComp through a stateful implementation in monad m can only shrink the support: any output reachable after simulation was already reachable in the original computation (where oracle queries may return any value). This is the support-level analogue of evalDist_simulateQ_run'_eq_evalDist.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Transcript count Q le of is Per Index Query Bound

OracleComp.transcript_countQ_le_of_isPerIndexQueryBound

Plain-language statement

Per-index query bound. If oa respects a per-index budget qb, then for every oracle index t the transcript contains at most qb t queries to t.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

View proof record