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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, ,  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
2instantiation5, 21, 17, 52, ,  ⊢  
  : , : , :
3instantiation6, 7,  ⊢  
  : , : , :
4instantiation8, 33, 32, 60, 35, 9, 21, 10, 11, ,  ⊢  
  : , : , : , : , : , :
5theorem  ⊢  
 proveit.numbers.exponentiation.pos_power_of_product
6axiom  ⊢  
 proveit.logic.equality.substitution
7instantiation12, 40, 46, 50, 22, 13, 14*,  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.disassociation
9instantiation43  ⊢  
  : , :
10instantiation16, 21, 15,  ⊢  
  : , :
11instantiation16, 17, 38,  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
13instantiation18, 19  ⊢  
  : , :
14instantiation20, 21  ⊢  
  :
15instantiation58, 49, 22  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
17instantiation58, 49, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.logic.equality.equals_reversal
19instantiation24, 25, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
21instantiation58, 49, 27  ⊢  
  : , : , :
22instantiation28, 46, 29  ⊢  
  : , :
23instantiation58, 54, 30  ⊢  
  : , : , :
24axiom  ⊢  
 proveit.logic.equality.equals_transitivity
25instantiation31, 60, 32, 33, 34, 35, 45, 38, 36  ⊢  
  : , : , : , : , : , :
26instantiation37, 45, 38, 39  ⊢  
  : , : , :
27instantiation58, 51, 40  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
29instantiation58, 54, 41  ⊢  
  : , : , :
30instantiation58, 56, 42  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.addition.disassociation
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
33axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
34instantiation43  ⊢  
  : , :
35theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36instantiation44, 45  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
38instantiation58, 49, 46  ⊢  
  : , : , :
39instantiation47  ⊢  
  :
40assumption  ⊢  
41instantiation58, 56, 48  ⊢  
  : , : , :
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44theorem  ⊢  
 proveit.numbers.negation.complex_closure
45instantiation58, 49, 50  ⊢  
  : , : , :
46instantiation58, 51, 52  ⊢  
  : , : , :
47axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
48instantiation53, 57  ⊢  
  :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation58, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
52assumption  ⊢  
53theorem  ⊢  
 proveit.numbers.negation.int_closure
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
55instantiation58, 56, 57  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
57instantiation58, 59, 60  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements