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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, ,  ⊢  
  : , : , :
1reference8  ⊢  
2instantiation8, 4, 5, ,  ⊢  
  : , : , :
3instantiation17, 6, 47, 20, 7, 13, 23, 24, 25, 26, 29, 27, 28, ,  ⊢  
  : , : , : , : , : , : , :
4instantiation8, 9, 10, ,  ⊢  
  : , : , :
5instantiation17, 11, 47, 46, 12, 13, 24, 25, 26, 29, 27, 28, ,  ⊢  
  : , : , : , : , : , : , :
6theorem  ⊢  
 proveit.numbers.numerals.decimals.nat7
7instantiation14  ⊢  
  : , : , : , : , : , : , :
8axiom  ⊢  
 proveit.logic.equality.equals_transitivity
9instantiation17, 46, 18, 15, 16, 24, 25, 26, 27, 28, 29, ,  ⊢  
  : , : , : , : , : , : , :
10instantiation17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, ,  ⊢  
  : , : , : , : , : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.nat6
12instantiation30  ⊢  
  : , : , : , : , : , :
13instantiation31  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
15instantiation32  ⊢  
  : , : , : , :
16instantiation32  ⊢  
  : , : , : , :
17theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
19theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
20axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
21instantiation32  ⊢  
  : , : , : , :
22instantiation33  ⊢  
  : , : , : , : , :
23theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24assumption  ⊢  
25instantiation48, 36, 34  ⊢  
  : , : , :
26instantiation48, 36, 35  ⊢  
  : , : , :
27assumption  ⊢  
28assumption  ⊢  
29instantiation48, 36, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
33theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
34instantiation48, 40, 38  ⊢  
  : , : , :
35instantiation48, 40, 39  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
37instantiation48, 40, 41  ⊢  
  : , : , :
38instantiation48, 44, 42  ⊢  
  : , : , :
39instantiation48, 44, 43  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation48, 44, 45  ⊢  
  : , : , :
42instantiation48, 49, 46  ⊢  
  : , : , :
43instantiation48, 49, 47  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation48, 49, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
48theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3