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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, 3*, 4*, , ,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2modus ponens5, 6, , ,  ⊢  
3instantiation7, 40  ⊢  
  : , :
4instantiation7, 40  ⊢  
  : , :
5instantiation8, 9  ⊢  
  : , : , : , : , : , : , :
6generalization10, , ,  ⊢  
7theorem  ⊢  
 proveit.core_expr_types.conditionals.satisfied_condition_reduction
8theorem  ⊢  
 proveit.core_expr_types.lambda_maps.general_lambda_substitution
9theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
10instantiation11, 12, 41, 13, 14, 15, 16, 17, 18, 19, , , ,  ⊢  
  : , : , : , : , : , : , : , : , : , :
11theorem  ⊢  
 proveit.linear_algebra.tensors.tensor_prod_association
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
13instantiation22  ⊢  
  : , :
14instantiation20, 21  ⊢  
  :
15instantiation22  ⊢  
  : , :
16assumption  ⊢  
17assumption  ⊢  
18instantiation23, 24,  ⊢  
  :
19assumption  ⊢  
20theorem  ⊢  
 proveit.linear_algebra.real_vec_set_is_vec_space
21theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
22theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23assumption  ⊢  
24instantiation25, 26, 27  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
26instantiation42, 28, 40  ⊢  
  : , : , :
27instantiation29, 30  ⊢  
  : , :
28instantiation31, 38, 39  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.ordering.relax_less
30instantiation32, 33, 34  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
32theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
33instantiation35, 36  ⊢  
  :
34instantiation37, 38, 39, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
37theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
38instantiation42, 43, 41  ⊢  
  : , : , :
39instantiation42, 43, 44  ⊢  
  : , : , :
40assumption  ⊢  
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
42theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
*equality replacement requirements