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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, , ,  ⊢  
  : , : , :
1reference10  ⊢  
2instantiation4, 5, 6, , ,  ⊢  
  : , : , :
3instantiation7, 67, 97, 69, 74, 63, 33, 8*, 9*,  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
5instantiation10, 11, 12,  ⊢  
  : , : , :
6instantiation13, 14, 15, 33, 16*, 17*, ,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_subtract
8instantiation18, 33,  ⊢  
  :
9instantiation19, 63, 77, 38, 20*, 21*,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
11instantiation22, 23, 83, 24, 25*  ⊢  
  : , : , : , :
12assumption  ⊢  
13theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
14instantiation26, 31, 27,  ⊢  
  :
15instantiation95, 28, 29  ⊢  
  : , : , :
16instantiation30, 31  ⊢  
  :
17instantiation32, 33,  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
19theorem  ⊢  
 proveit.numbers.exponentiation.product_of_posnat_powers
20instantiation34, 63  ⊢  
  :
21instantiation49, 35, 36  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.numbers.summation.sum_split_last
23theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
24instantiation37, 38  ⊢  
  :
25instantiation49, 39, 40  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
27instantiation41, 42  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29instantiation95, 43, 44  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
31instantiation45, 74, 46  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.division.frac_one_denom
33instantiation47, 63, 48,  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
35instantiation54, 97, 68, 67, 55, 69, 74, 71  ⊢  
  : , : , : , : , : , :
36instantiation49, 50, 51  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38instantiation52, 97, 67, 69, 94, 53  ⊢  
  : , : , : , : , :
39instantiation54, 67, 68, 97, 69, 55, 71, 74, 56  ⊢  
  : , : , : , : , : , :
40instantiation57, 74, 71, 58  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
42instantiation59, 60  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
44instantiation95, 61, 62  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
46instantiation73, 63  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
48instantiation95, 81, 64  ⊢  
  : , : , :
49axiom  ⊢  
 proveit.logic.equality.equals_transitivity
50instantiation65, 97, 67, 69, 74, 71  ⊢  
  : , : , : , : , : , : , :
51instantiation66, 67, 68, 97, 69, 70, 74, 71, 72*  ⊢  
  : , : , : , : , : , :
52theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_from_nonneg
53theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
54theorem  ⊢  
 proveit.numbers.addition.disassociation
55instantiation79  ⊢  
  : , :
56instantiation73, 74  ⊢  
  :
57theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
58instantiation75  ⊢  
  :
59theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
60assumption  ⊢  
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
62instantiation95, 76, 77  ⊢  
  : , : , :
63assumption  ⊢  
64instantiation95, 86, 78  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
66theorem  ⊢  
 proveit.numbers.addition.association
67axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
68theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
69theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
70instantiation79  ⊢  
  : , :
71instantiation95, 81, 80  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
73theorem  ⊢  
 proveit.numbers.negation.complex_closure
74instantiation95, 81, 82  ⊢  
  : , : , :
75axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
77theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
78instantiation95, 92, 83  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
80instantiation84, 85, 94  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
82instantiation95, 86, 87  ⊢  
  : , : , :
83instantiation88, 89, 93  ⊢  
  : , :
84theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
85instantiation90, 91  ⊢  
  : , :
86theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
87instantiation95, 92, 93  ⊢  
  : , : , :
88theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
89instantiation95, 96, 94  ⊢  
  : , : , :
90theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
91theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_within_real
92theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
93instantiation95, 96, 97  ⊢  
  : , : , :
94assumption  ⊢  
95theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
96theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
97theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements