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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,  ⊢  
  : , : , :
1reference5  ⊢  
2instantiation28, 3, 4,  ⊢  
  : , : , :
3instantiation5, 6,  ⊢  
  : , : , :
4instantiation7, 8,  ⊢  
  : , :
5axiom  ⊢  
 proveit.logic.equality.substitution
6instantiation9, 37, 10, 34, 38, 11, 44, 45, 41, 42, 12,  ⊢  
  : , : , : , : , : , :
7theorem  ⊢  
 proveit.logic.equality.equals_reversal
8instantiation13, 14, 15, 16,  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.multiplication.association
10theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
11instantiation17  ⊢  
  : , : , : , :
12instantiation58, 49, 18  ⊢  
  : , : , :
13instantiation19, 33  ⊢  
  :
14instantiation58, 49, 20  ⊢  
  : , : , :
15instantiation21, 22, 23  ⊢  
  : , : , :
16instantiation24, 25  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
18instantiation58, 52, 26  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.exponentiation.int_exp_of_exp
20instantiation58, 54, 32  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
22instantiation43, 35, 27  ⊢  
  : , :
23instantiation28, 29, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
25instantiation58, 31, 32  ⊢  
  : , : , :
26instantiation58, 56, 33  ⊢  
  : , : , :
27instantiation43, 41, 42  ⊢  
  : , :
28axiom  ⊢  
 proveit.logic.equality.equals_transitivity
29instantiation36, 34, 60, 37, 40, 38, 35, 41, 42  ⊢  
  : , : , : , : , : , :
30instantiation36, 37, 60, 38, 39, 40, 44, 45, 41, 42  ⊢  
  : , : , : , : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
33assumption  ⊢  
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
35instantiation43, 44, 45  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.multiplication.disassociation
37axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
38theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39instantiation46  ⊢  
  : , :
40instantiation46  ⊢  
  : , :
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
42instantiation58, 49, 47  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
44instantiation58, 49, 48  ⊢  
  : , : , :
45instantiation58, 49, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47instantiation58, 54, 51  ⊢  
  : , : , :
48instantiation58, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation58, 54, 55  ⊢  
  : , : , :
51assumption  ⊢  
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation58, 56, 57  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
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.nat2