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Show the Proof

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
0instantiation1, 2,  ⊢  
  : , :
1theorem  ⊢  
 proveit.logic.equality.equals_reversal
2modus ponens3, 4,  ⊢  
3instantiation5, 6, 7, 8, 9, 10  ⊢  
  : , : , : , : , : , : , : , : , : , :
4generalization11,  ⊢  
5theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
6theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
7theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
8axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
9instantiation12, 35, 14, 15  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11instantiation13, 35, 14, 15, 16, 17, 18, ,  ⊢  
  : , : , : , :
12theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
13theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
14instantiation21  ⊢  
  : , :
15instantiation19, 20  ⊢  
  :
16instantiation21  ⊢  
  : , :
17assumption  ⊢  
18instantiation22, 23,  ⊢  
  :
19theorem  ⊢  
 proveit.linear_algebra.real_vec_set_is_vec_space
20theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
21theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22assumption  ⊢  
23instantiation24, 25, 26  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
25instantiation41, 27, 39  ⊢  
  : , : , :
26instantiation28, 29  ⊢  
  : , :
27instantiation30, 37, 38  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.ordering.relax_less
29instantiation31, 32, 33  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
31theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
32instantiation34, 35  ⊢  
  :
33instantiation36, 37, 38, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
35theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
36theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
37instantiation41, 42, 40  ⊢  
  : , : , :
38instantiation41, 42, 43  ⊢  
  : , : , :
39assumption  ⊢  
40theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
41theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4