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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,  ⊢  
  : , : , :
1reference19  ⊢  
2instantiation19, 4, 5  ⊢  
  : , : , :
3assumption  ⊢  
4instantiation6, 82, 7, 8, 9*  ⊢  
  : , : , : , :
5instantiation10, 85, 60, 59, 62, 61, 23, 65, 69  ⊢  
  : , : , : , : , : , :
6axiom  ⊢  
 proveit.numbers.summation.sum_split_last
7instantiation11, 53, 82  ⊢  
  : , :
8instantiation12, 73, 13, 70, 14, 15*  ⊢  
  : , : , :
9instantiation54, 16, 17  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.addition.association
11theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
12theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
14instantiation18, 76  ⊢  
  :
15instantiation19, 20, 21  ⊢  
  : , : , :
16instantiation50, 22  ⊢  
  : , : , :
17instantiation58, 85, 60, 59, 62, 61, 23, 65, 69  ⊢  
  : , : , : , : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
19theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
20instantiation24, 69  ⊢  
  :
21instantiation25, 69, 26  ⊢  
  : , :
22instantiation27, 28, 29, 30, 31, 32  ⊢  
  : , : , :
23modus ponens33, 34  ⊢  
24theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
25theorem  ⊢  
 proveit.numbers.addition.commutation
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
27theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
28theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
29instantiation67  ⊢  
  : , :
30instantiation67  ⊢  
  : , :
31instantiation50, 35  ⊢  
  : , : , :
32instantiation71  ⊢  
  :
33instantiation36  ⊢  
  : , : , :
34generalization37  ⊢  
35modus ponens38, 39  ⊢  
36theorem  ⊢  
 proveit.numbers.summation.summation_complex_closure
37instantiation83, 72, 40,  ⊢  
  : , : , :
38instantiation41, 42  ⊢  
  : , : , : , : , : , :
39generalization43  ⊢  
40instantiation83, 77, 44,  ⊢  
  : , : , :
41axiom  ⊢  
 proveit.core_expr_types.lambda_maps.lambda_substitution
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
43instantiation50, 45  ⊢  
  : , : , :
44instantiation83, 81, 46,  ⊢  
  : , : , :
45instantiation50, 47  ⊢  
  : , : , :
46instantiation83, 48, 49,  ⊢  
  : , : , :
47instantiation50, 51  ⊢  
  : , : , :
48instantiation52, 82, 53  ⊢  
  : , :
49assumption  ⊢  
50axiom  ⊢  
 proveit.logic.equality.substitution
51instantiation54, 55, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
53instantiation83, 57, 76  ⊢  
  : , : , :
54axiom  ⊢  
 proveit.logic.equality.equals_transitivity
55instantiation58, 59, 60, 85, 61, 62, 65, 69, 63  ⊢  
  : , : , : , : , : , :
56instantiation64, 69, 65, 66  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
58theorem  ⊢  
 proveit.numbers.addition.disassociation
59axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
61theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
62instantiation67  ⊢  
  : , :
63instantiation68, 69  ⊢  
  :
64theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
65instantiation83, 72, 70  ⊢  
  : , : , :
66instantiation71  ⊢  
  :
67theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68theorem  ⊢  
 proveit.numbers.negation.complex_closure
69instantiation83, 72, 73  ⊢  
  : , : , :
70instantiation74, 75, 76  ⊢  
  : , : , :
71axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
72theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
73instantiation83, 77, 78  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
75instantiation79, 80  ⊢  
  : , :
76assumption  ⊢  
77theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
78instantiation83, 81, 82  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
80theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
81theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
82instantiation83, 84, 85  ⊢  
  : , : , :
83theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
85theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements