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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, ,  ⊢  
  : , : , :
1reference35  ⊢  
2instantiation35, 4, 5, ,  ⊢  
  : , : , :
3instantiation6, 42, 43, 69, 44, 7, 12, 13, 31, ,  ⊢  
  : , : , : , : , : , :
4instantiation35, 8, 9, ,  ⊢  
  : , : , :
5instantiation10, 69, 43, 42, 11, 44, 12, 13, 31, ,  ⊢  
  : , : , : , : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.association
7instantiation53  ⊢  
  : , :
8instantiation35, 14, 15, ,  ⊢  
  : , : , :
9instantiation19, 16,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11instantiation53  ⊢  
  : , :
12instantiation17, 27, 48,  ⊢  
  : , :
13instantiation17, 31, 18,  ⊢  
  : , :
14instantiation19, 20,  ⊢  
  : , : , :
15instantiation21, 27, 31, 62, ,  ⊢  
  : , : , :
16instantiation22, 50, 56, 25, 60, 23, 24*,  ⊢  
  : , : , : , :
17theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
18instantiation67, 59, 25  ⊢  
  : , : , :
19axiom  ⊢  
 proveit.logic.equality.substitution
20instantiation26, 31, 27,  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.pos_power_of_product
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
23instantiation28, 29  ⊢  
  : , :
24instantiation30, 31  ⊢  
  :
25instantiation32, 56, 33  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.multiplication.commutation
27instantiation67, 59, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.logic.equality.equals_reversal
29instantiation35, 36, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
31instantiation67, 59, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
33instantiation67, 63, 39  ⊢  
  : , : , :
34instantiation67, 63, 40  ⊢  
  : , : , :
35axiom  ⊢  
 proveit.logic.equality.equals_transitivity
36instantiation41, 42, 43, 69, 44, 45, 48, 46, 55  ⊢  
  : , : , : , : , : , :
37instantiation47, 55, 48, 49  ⊢  
  : , : , :
38instantiation67, 61, 50  ⊢  
  : , : , :
39instantiation67, 65, 51  ⊢  
  : , : , :
40instantiation67, 65, 52  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.addition.disassociation
42axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
44theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45instantiation53  ⊢  
  : , :
46instantiation54, 55  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
48instantiation67, 59, 56  ⊢  
  : , : , :
49instantiation57  ⊢  
  :
50assumption  ⊢  
51instantiation58, 66  ⊢  
  :
52assumption  ⊢  
53theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
54theorem  ⊢  
 proveit.numbers.negation.complex_closure
55instantiation67, 59, 60  ⊢  
  : , : , :
56instantiation67, 61, 62  ⊢  
  : , : , :
57axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
58theorem  ⊢  
 proveit.numbers.negation.int_closure
59theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
60instantiation67, 63, 64  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
62assumption  ⊢  
63theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
64instantiation67, 65, 66  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
66instantiation67, 68, 69  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements