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/top,top_limits,lim_of_functions,convergence_functions,epsilon_lemmas,lim_of_composition,continuous_functions,top_sequences,convergence_ops,convergence_sequences,sequence_props,real_fun_supinf,monotone_subsequence,top_continuity,composition_continuous,restriction_continuous,restriction_cont_fun,restriction_continuous2,continuous_functions_props,continuity_interval,continuity_props,interm_value_thm,continuous_functions_more,unif_cont_fun,deriv_domain_def,inverse_continuous_functions,continuous_linear,linear_functions,cont_if_fun,continuous_lambda,sqrt_derivative,derivative_inverse,derivatives,derivatives_def,derivative_props,derivatives_alt,chain_rule,real_fun_continuity_equiv,real_metric_space,metric_spaces_def,open_sets,compactness,metric_spaces,prelude_sets_aux,continuity_ms_def,weierstrass_approximation,real_fun_on_compact_sets,uniform_continuity,continuity_ms,finite_sets_aux,top_metric_spaces,cross_metric_spaces,cross_metric_cont,cross_metric_uniform_continuity,cross_metric_real_fun,continuity_of_max_min,ms_composition_cont,metric_space_real_fun,inverse_fun_ms_continuous,convex_function_props,top_derivative,derivatives_lam,deriv_domain,deriv_domains,deriv_sign,derivatives_subtype,restrict2_deriv,polynomial_deriv,nth_derivatives,taylors,top_riesz_representation,bounded_variation,rs_partition,riesz_bounded_functionals,riesz_function_sets,riesz_interval_funs,riesz_linear_functionals,riesz_hahn_banach,riesz_representation,rs_integral_cont,rs_integral_prep,rs_integral_def,top_integral,integral,integral_def,integral_cont,integral_cont_scaf,integral_prep,integral_step,step_fun_def,integral_pulse,interval_minmax,integral_split,integral_split_scaf,integral_bounded,step_fun_props,step_fun_scaf,partitions_scaf,fundamental_theorem,table_of_integrals,indefinite_integral,integral_chg_var,integral_diff_doms,integral_mean_value,integration_by_parts
structures/sort_array,for_iterate,permutations,min_array_def,fseqs_ops,min_seq,sort_seq,max_array_def,below_arrays,fseqs,fsq,seqs,concat_arrays,sort_seq_lems,permutations_fseq,max_seq,sort_fseq,permutations_seq,sort_array_def
reals/binomial_identities,real_fun_preds,bound_defs,factorial,binomial,sigma_below_sub,abs_lems,sign,sqrt_exists,root,polynomials,convex_functions,real_fun_ops,sigma_below,bounded_reals,intervals_real,quadratic,real_fun_props,sigma_upto,sigma_swap,min_max,real_facts,connected_set,product,bernstein_polynomials,sigma,sqrt,reals_complete_more,sq,sigma_nat
orders/relations_extra,bounded_orders,minmax_orders,chain_chain,ordered_subset,relation_iterate,zorn,chain,indexed_sets_extra,subset_chain,closure_ops
finite_sets/func_composition,finite_sets_minmax,finite_sets_inductions,finite_sets_card_eq,finite_sets_below
ints/factorial,max_below
top:top_limits,top_sequences,top_continuity,top_metric_spaces,top_derivative,top_riesz_representation,top_integral
top_limits:lim_of_functions,lim_of_composition
lim_of_functions:convergence_functions
convergence_functions:reals@real_fun_ops,epsilon_lemmas
epsilon_lemmas:reals@real_facts,reals@abs_lems
lim_of_composition:lim_of_functions,continuous_functions
continuous_functions:lim_of_functions
top_sequences:convergence_ops,convergence_sequences
convergence_ops:convergence_sequences,epsilon_lemmas
convergence_sequences:sequence_props,reals@abs_lems,monotone_subsequence
sequence_props:real_fun_supinf
real_fun_supinf:reals@real_fun_props,reals@real_facts
monotone_subsequence:sequence_props
top_continuity:continuous_functions,composition_continuous,restriction_continuous,restriction_cont_fun,restriction_continuous2,continuous_functions_props,continuity_interval,interm_value_thm,continuous_functions_more,unif_cont_fun,inverse_continuous_functions,continuous_linear,cont_if_fun,continuous_lambda,real_fun_continuity_equiv,weierstrass_approximation
composition_continuous:continuous_functions,reals@real_fun_props
restriction_continuous:continuous_functions
restriction_cont_fun:continuous_functions
restriction_continuous2:continuous_functions
continuous_functions_props:continuity_interval
continuity_interval:continuity_props
continuity_props:continuous_functions,top_sequences
interm_value_thm:continuity_interval,reals@intervals_real,reals@connected_set
continuous_functions_more:continuous_functions,convergence_sequences,unif_cont_fun
unif_cont_fun:deriv_domain_def,continuous_functions,convergence_sequences
deriv_domain_def:
inverse_continuous_functions:continuous_functions_props
continuous_linear:continuous_functions,linear_functions
linear_functions:reals@real_fun_props
cont_if_fun:continuous_functions
continuous_lambda:continuous_functions,reals@min_max,sqrt_derivative,composition_continuous
sqrt_derivative:reals@sq,reals@sqrt,derivative_inverse
derivative_inverse:deriv_domain_def,derivatives,derivative_props,chain_rule,inverse_continuous_functions,lim_of_functions,composition_continuous
derivatives:deriv_domain_def,derivatives_def
derivatives_def:deriv_domain_def,lim_of_functions,continuous_functions
derivative_props:deriv_domain_def,derivatives_alt,continuous_functions_props
derivatives_alt:deriv_domain_def,derivatives,continuous_functions_props
chain_rule:deriv_domain_def,derivative_props,lim_of_composition
real_fun_continuity_equiv:real_metric_space,continuous_functions,continuity_ms_def
real_metric_space:metric_spaces_def,open_sets,compactness,convergence_sequences
metric_spaces_def:
open_sets:reals@intervals_real
compactness:metric_spaces_def,metric_spaces,finite_sets@finite_sets_minmax
metric_spaces:metric_spaces_def,prelude_sets_aux
prelude_sets_aux:
continuity_ms_def:metric_spaces_def,metric_spaces
weierstrass_approximation:reals@bernstein_polynomials,real_fun_continuity_equiv,real_fun_on_compact_sets,uniform_continuity,reals@sqrt
real_fun_on_compact_sets:metric_spaces_def,real_metric_space,continuity_ms_def,reals@abs_lems,compactness
uniform_continuity:metric_spaces_def,continuity_ms,compactness,finite_sets_aux,finite_sets@finite_sets_minmax,prelude_sets_aux
continuity_ms:metric_spaces,continuity_ms_def,compactness
finite_sets_aux:
top_metric_spaces:uniform_continuity,compactness,cross_metric_spaces,cross_metric_cont,continuity_ms_def,continuity_ms,cross_metric_uniform_continuity,metric_spaces,cross_metric_real_fun,real_fun_on_compact_sets,real_metric_space,continuity_of_max_min,ms_composition_cont,metric_space_real_fun,inverse_fun_ms_continuous,convex_function_props
cross_metric_spaces:metric_spaces,reals@sqrt,reals@sq
cross_metric_cont:metric_spaces,cross_metric_spaces,continuity_ms_def,uniform_continuity
cross_metric_uniform_continuity:metric_spaces,cross_metric_spaces,continuity_ms_def,cross_metric_cont,compactness
cross_metric_real_fun:metric_spaces,real_metric_space,cross_metric_uniform_continuity,continuity_ms,real_fun_on_compact_sets,reals@bounded_reals
continuity_of_max_min:metric_spaces_def,real_metric_space,continuity_ms_def,reals@abs_lems,compactness
ms_composition_cont:metric_spaces,continuity_ms
metric_space_real_fun:metric_spaces_def,real_metric_space,continuity_ms_def,reals@abs_lems
inverse_fun_ms_continuous:metric_spaces,uniform_continuity,continuity_ms
convex_function_props:real_metric_space,continuity_ms_def,reals@convex_functions
top_derivative:derivatives,derivative_props,derivatives_lam,chain_rule,deriv_domain,deriv_domains,deriv_sign,derivatives_subtype,restrict2_deriv,sqrt_derivative,derivative_inverse,polynomial_deriv,nth_derivatives,taylors
derivatives_lam:deriv_domain_def,derivatives
deriv_domain:deriv_domain_def,reals@intervals_real
deriv_domains:deriv_domain
deriv_sign:deriv_domain,derivatives,reals@sign
derivatives_subtype:deriv_domain_def,derivatives
restrict2_deriv:deriv_domain_def,derivatives,chain_rule
polynomial_deriv:reals@sigma,derivatives,chain_rule,derivative_props,convergence_ops,ints@factorial,nth_derivatives,reals@binomial,reals@polynomials
nth_derivatives:deriv_domain_def,derivatives
taylors:deriv_domain_def,reals@sigma_nat,ints@factorial,derivatives,nth_derivatives,derivative_props
top_riesz_representation:bounded_variation,riesz_bounded_functionals,riesz_function_sets,riesz_hahn_banach,riesz_interval_funs,riesz_linear_functionals,riesz_representation,rs_integral_cont,rs_integral_def,rs_integral_prep,rs_partition
bounded_variation:deriv_domain_def,rs_partition,reals@real_fun_preds
rs_partition:deriv_domain_def,finite_sets@finite_sets_minmax,structures@sort_fseq,structures@fseqs_ops,reals@intervals_real,reals@sigma_below,reals@sigma_upto
riesz_bounded_functionals:riesz_linear_functionals,riesz_function_sets
riesz_function_sets:riesz_interval_funs
riesz_interval_funs:real_metric_space,real_fun_on_compact_sets,metric_space_real_fun
riesz_linear_functionals:riesz_function_sets,real_metric_space
riesz_hahn_banach:riesz_interval_funs,riesz_bounded_functionals,orders@zorn
riesz_representation:riesz_interval_funs,rs_integral_cont,riesz_hahn_banach,bounded_variation,reals@sign,riesz_bounded_functionals
rs_integral_cont:deriv_domain_def,real_metric_space,uniform_continuity,rs_integral_prep,bounded_variation
rs_integral_prep:deriv_domain_def,rs_integral_def,reals@real_fun_ops,continuous_functions,convergence_sequences
rs_integral_def:deriv_domain_def,rs_partition,reals@real_fun_preds,reals@intervals_real
top_integral:integral,fundamental_theorem,table_of_integrals,integral_chg_var,integral_diff_doms,integral_mean_value,integration_by_parts,indefinite_integral
integral:deriv_domain_def,integral_def,integral_cont,integral_split,reals@real_fun_ops,continuous_functions_more
integral_def:deriv_domain_def,finite_sets@finite_sets_minmax,reals@intervals_real,reals@sigma_below,reals@sigma_upto
integral_cont:deriv_domain_def,integral_cont_scaf,continuous_functions
integral_cont_scaf:deriv_domain_def,integral_prep,integral_step,interval_minmax,unif_cont_fun,continuity_interval
integral_prep:deriv_domain_def,integral_def,reals@real_fun_ops,continuous_functions,convergence_sequences
integral_step:deriv_domain_def,step_fun_def,integral_pulse
step_fun_def:deriv_domain_def,integral_def
integral_pulse:deriv_domain_def,integral_prep,reals@sigma_upto
interval_minmax:deriv_domain_def,continuity_interval,reals@intervals_real
integral_split:deriv_domain_def,integral_split_scaf,step_fun_props,reals@sigma_below,structures@concat_arrays,reals@sigma_below_sub
integral_split_scaf:deriv_domain_def,reals@sigma_below,step_fun_def,integral_step,integral_bounded
integral_bounded:deriv_domain_def,reals@sigma_below,integral_prep
step_fun_props:deriv_domain_def,step_fun_def,reals@sigma_below,structures@sort_seq_lems,step_fun_scaf
step_fun_scaf:deriv_domain_def,integral_step,partitions_scaf
partitions_scaf:deriv_domain_def,integral_def,structures@sort_seq_lems,finite_sets@finite_sets_minmax,ints@max_below
fundamental_theorem:deriv_domain_def,integral,derivative_props
table_of_integrals:deriv_domain_def,fundamental_theorem,indefinite_integral
indefinite_integral:deriv_domain_def,integral,derivative_props,fundamental_theorem
integral_chg_var:deriv_domain_def,composition_continuous,fundamental_theorem,chain_rule
integral_diff_doms:deriv_domain_def,integral
integral_mean_value:deriv_domain_def,fundamental_theorem
integration_by_parts:deriv_domain_def,fundamental_theorem