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In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0modus ponens1, 2,  ⊢  
1instantiation3, 4, 5, 6, 7, 8  ⊢  
  : , : , : , : , : , : , : , : , : , :
2generalization9,  ⊢  
3theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
4theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
5theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
6axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
7instantiation10, 33, 12, 13  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9instantiation11, 33, 12, 13, 14, 15, 16, ,  ⊢  
  : , : , : , :
10theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
11theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
12instantiation19  ⊢  
  : , :
13instantiation17, 18  ⊢  
  :
14instantiation19  ⊢  
  : , :
15assumption  ⊢  
16instantiation20, 21,  ⊢  
  :
17theorem  ⊢  
 proveit.linear_algebra.real_vec_set_is_vec_space
18theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
19theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20assumption  ⊢  
21instantiation22, 23, 24  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
23instantiation39, 25, 37  ⊢  
  : , : , :
24instantiation26, 27  ⊢  
  : , :
25instantiation28, 35, 36  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.ordering.relax_less
27instantiation29, 30, 31  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
29theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
30instantiation32, 33  ⊢  
  :
31instantiation34, 35, 36, 37  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
34theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
35instantiation39, 40, 38  ⊢  
  : , : , :
36instantiation39, 40, 41  ⊢  
  : , : , :
37assumption  ⊢  
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
39theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4