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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,  ⊢  
  : , : , :
1reference32  ⊢  
2instantiation4, 5,  ⊢  
  : , : , :
3instantiation6, 7,  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation32, 8, 9,  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.logic.equality.equals_reversal
7instantiation10, 11, 12, 13,  ⊢  
  : , :
8instantiation14, 15, 38, 41, 16, 42, 49, 50, 45, 20, 46,  ⊢  
  : , : , : , : , : , : , :
9instantiation17, 41, 18, 38, 42, 19, 49, 50, 45, 46, 20,  ⊢  
  : , : , : , : , : , :
10instantiation21, 47  ⊢  
  :
11instantiation64, 54, 22  ⊢  
  : , : , :
12instantiation23, 24, 25  ⊢  
  : , : , :
13instantiation26, 27  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.multiplication.rightward_commutation
15theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
16instantiation28  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.association
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
19instantiation29  ⊢  
  : , : , : , :
20instantiation64, 54, 30  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.int_exp_of_exp
22instantiation64, 59, 36  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
24instantiation48, 39, 31  ⊢  
  : , :
25instantiation32, 33, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
27instantiation64, 35, 36  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
30instantiation64, 57, 37  ⊢  
  : , : , :
31instantiation48, 45, 46  ⊢  
  : , :
32axiom  ⊢  
 proveit.logic.equality.equals_transitivity
33instantiation40, 38, 66, 41, 44, 42, 39, 45, 46  ⊢  
  : , : , : , : , : , :
34instantiation40, 41, 66, 42, 43, 44, 49, 50, 45, 46  ⊢  
  : , : , : , : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
37instantiation64, 62, 47  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
39instantiation48, 49, 50  ⊢  
  : , :
40theorem  ⊢  
 proveit.numbers.multiplication.disassociation
41axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
42theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
43instantiation51  ⊢  
  : , :
44instantiation51  ⊢  
  : , :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
46instantiation64, 54, 52  ⊢  
  : , : , :
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
49instantiation64, 54, 53  ⊢  
  : , : , :
50instantiation64, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52instantiation64, 57, 56  ⊢  
  : , : , :
53instantiation64, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
55instantiation64, 59, 60  ⊢  
  : , : , :
56instantiation64, 62, 61  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
58instantiation64, 62, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
61assumption  ⊢  
62theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
63instantiation64, 65, 66  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2