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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,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 55, 56, 5, 38, 39, 42, 21, 22, 6,  ⊢  
  : , : , : , : , : , : , : , :
3instantiation7, 8, 9, 10,  ⊢  
  : , : , : , :
4theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
5instantiation11  ⊢  
  : , : , :
6instantiation12  ⊢  
  :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation13, 59, 34, 14, 19, 35, 38, 42, 21, 22,  ⊢  
  : , : , : , : , : , : , :
9instantiation17, 55, 59, 15, 19, 38, 42, 21, 22, 16*,  ⊢  
  : , : , : , : , : , :
10instantiation17, 59, 34, 18, 19, 35, 38, 20, 21, 22, 23*,  ⊢  
  : , : , : , : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
13theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
14instantiation43  ⊢  
  : , :
15instantiation43  ⊢  
  : , :
16instantiation27, 24, 25*  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.addition.association
18instantiation43  ⊢  
  : , :
19instantiation43  ⊢  
  : , :
20instantiation26, 38, 42  ⊢  
  : , :
21instantiation26, 37, 39  ⊢  
  : , :
22instantiation26, 38, 39  ⊢  
  : , :
23instantiation27, 28, 29*  ⊢  
  : , :
24instantiation33, 34, 59, 55, 35, 30, 31, 42, 32*  ⊢  
  : , : , : , : , : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
26theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
27theorem  ⊢  
 proveit.logic.equality.equals_reversal
28instantiation33, 34, 59, 55, 35, 36, 37, 38, 39  ⊢  
  : , : , : , : , : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.add_3_2
30instantiation43  ⊢  
  : , :
31instantiation57, 45, 40  ⊢  
  : , : , :
32instantiation41, 42  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
34axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
35theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36instantiation43  ⊢  
  : , :
37instantiation57, 45, 44  ⊢  
  : , : , :
38instantiation57, 45, 46  ⊢  
  : , : , :
39assumption  ⊢  
40instantiation57, 49, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44instantiation57, 49, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46instantiation57, 49, 50  ⊢  
  : , : , :
47instantiation57, 53, 51  ⊢  
  : , : , :
48instantiation57, 53, 52  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
50instantiation57, 53, 54  ⊢  
  : , : , :
51instantiation57, 58, 55  ⊢  
  : , : , :
52instantiation57, 58, 56  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
54instantiation57, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements