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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  ⊢  
  : , : , : , :
1reference22  ⊢  
2instantiation5, 6, 7  ⊢  
  : , : , :
3reference61  ⊢  
4instantiation8, 9  ⊢  
  : , :
5theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
6instantiation10, 11  ⊢  
  : , : , :
7instantiation12, 13, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.logic.equality.equals_reversal
9instantiation15, 16  ⊢  
  : , :
10theorem  ⊢  
 proveit.core_expr_types.tuples.range_len
11instantiation17, 37, 18, 36, 19, 78  ⊢  
  : , :
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation20, 21  ⊢  
  : , : , :
14instantiation22, 23, 24, 25  ⊢  
  : , : , : , :
15theorem  ⊢  
 proveit.core_expr_types.tuples.range_from1_len
16instantiation81, 26, 83  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.addition.add_nat_closure
18instantiation48  ⊢  
  : , : , :
19instantiation27, 28  ⊢  
  :
20axiom  ⊢  
 proveit.logic.equality.substitution
21instantiation29, 58, 57, 30*  ⊢  
  : , :
22theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
23instantiation31, 78, 32, 33, 34, 60, 40, 57  ⊢  
  : , : , : , : , : , :
24instantiation35, 36, 37, 38, 39, 60, 40, 57  ⊢  
  : , : , : , :
25instantiation41, 57, 60, 42  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
27theorem  ⊢  
 proveit.numbers.negation.nat_closure
28instantiation43, 44, 45  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
30instantiation46, 60  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.addition.disassociation
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
33instantiation47  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
35theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
36axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
38theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39instantiation48  ⊢  
  : , : , :
40instantiation49, 57  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
42instantiation66  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
44instantiation50, 74, 72  ⊢  
  : , :
45instantiation51, 63, 62, 65, 52, 53*, 54*  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.negation.double_negation
47theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
49theorem  ⊢  
 proveit.numbers.negation.complex_closure
50theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
51theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
52instantiation55, 83  ⊢  
  :
53instantiation56, 57, 58  ⊢  
  : , :
54instantiation59, 60, 61  ⊢  
  : , :
55theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
56theorem  ⊢  
 proveit.numbers.addition.commutation
57instantiation81, 64, 62  ⊢  
  : , : , :
58instantiation81, 64, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_basic
60instantiation81, 64, 65  ⊢  
  : , : , :
61instantiation66  ⊢  
  :
62instantiation81, 68, 67  ⊢  
  : , : , :
63instantiation81, 68, 69  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
65instantiation70, 71, 83  ⊢  
  : , : , :
66axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
67instantiation81, 73, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
69instantiation81, 73, 74  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
71instantiation75, 76  ⊢  
  : , :
72instantiation81, 77, 78  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
74instantiation79, 80  ⊢  
  :
75theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
78theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
79theorem  ⊢  
 proveit.numbers.negation.int_closure
80instantiation81, 82, 83  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
83assumption  ⊢  
*equality replacement requirements