Theorem: selectColumns1_spec1 (Table/Proofs.lean)

State before:
η : Type u_η
dec_η : DecidableEq η
sch : Schema
⊢ ∀ (t : Table sch) (bs : List Bool), header (selectColumns1 t bs) <+ header t
Tactic:
intro t bs
State after:
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ header (selectColumns1 t bs) <+ header t

State before:
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ header (selectColumns1 t bs) <+ header t
Tactic:
simp only [header, Schema.names, Schema.sieve_eq_List_sieve]
State after:
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.map Prod.fst (List.sieve bs sch) <+ List.map Prod.fst sch

State before:
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
bs : List Bool
⊢ List.map Prod.fst (List.sieve bs sch) <+ List.map Prod.fst sch
Tactic:
exact List.sublist_of_map_sublist _ _ Prod.fst $ List.sieve_sublist bs sch
State after:
no goals