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Commit 2019-01-23 11:48 96198b98

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feat(contraction_mapping): proof the Banach fixed-point theorem (closes #553)

Estimated changes

Modified src/algebra/pi_instances.lean

added def prod.prod_semilattice_sup

Created src/contraction_mapping.lean

added theorem continuous_prod_snd

added theorem dist_bound_of_contraction

added theorem dist_inequality_of_contraction

added theorem fixed_point_exists_of_contraction

added theorem fixed_point_of_iteration_limit

added theorem fixed_point_unique_of_contraction

added theorem iterated_lipschitz_of_lipschitz

added def lipschitz

added theorem tendsto_dist_bound_at_top_nhds_0

added theorem uniform_continuous_of_lipschitz

Modified src/data/prod.lean

added theorem prod.map_def

Modified src/order/filter.lean

added theorem filter.prod_at_top_at_top_eq

added theorem filter.prod_map_at_top_eq

Modified src/topology/metric_space/basic.lean

added theorem cauchy_seq_iff_tendsto_dist_at_top_0

added theorem dist_prod_eq_dist_0

Modified src/topology/uniform_space/basic.lean

added theorem cauchy_seq_iff_prod_map