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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, 5, 6, 7, 8*, 9*  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.core_expr_types.tuples.general_len
2theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
3instantiation50  ⊢  
  : , :
4instantiation50  ⊢  
  : , :
5instantiation50  ⊢  
  : , :
6instantiation10, 76, 11  ⊢  
  : , : , :
7instantiation12, 38, 13, 37, 14, 76  ⊢  
  : , :
8reference11  ⊢  
9instantiation15, 16, 17  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
11instantiation18, 55, 43  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.addition.add_nat_closure
13instantiation51  ⊢  
  : , : , :
14instantiation19, 20  ⊢  
  :
15axiom  ⊢  
 proveit.logic.equality.equals_transitivity
16instantiation21, 22  ⊢  
  : , : , :
17instantiation23, 24, 25, 26  ⊢  
  : , : , : , :
18theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_12
19theorem  ⊢  
 proveit.numbers.negation.nat_closure
20instantiation27, 28, 29  ⊢  
  :
21axiom  ⊢  
 proveit.logic.equality.substitution
22instantiation30, 56, 55, 31*  ⊢  
  : , :
23theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
24instantiation32, 76, 33, 34, 35, 58, 41, 55  ⊢  
  : , : , : , : , : , :
25instantiation36, 37, 38, 39, 40, 58, 41, 55  ⊢  
  : , : , : , :
26instantiation42, 55, 58, 43  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
28instantiation44, 72, 70  ⊢  
  : , :
29instantiation45, 61, 60, 63, 46, 47*, 48*  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
31instantiation49, 58  ⊢  
  :
32theorem  ⊢  
 proveit.numbers.addition.disassociation
33theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
34instantiation50  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
36theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
37axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
39theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40instantiation51  ⊢  
  : , : , :
41instantiation52, 55  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_32
43instantiation64  ⊢  
  :
44theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
45theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
46instantiation53, 81  ⊢  
  :
47instantiation54, 55, 56  ⊢  
  : , :
48instantiation57, 58, 59  ⊢  
  : , :
49theorem  ⊢  
 proveit.numbers.negation.double_negation
50theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
51theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
52theorem  ⊢  
 proveit.numbers.negation.complex_closure
53theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
54theorem  ⊢  
 proveit.numbers.addition.commutation
55instantiation79, 62, 60  ⊢  
  : , : , :
56instantiation79, 62, 61  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_basic
58instantiation79, 62, 63  ⊢  
  : , : , :
59instantiation64  ⊢  
  :
60instantiation79, 66, 65  ⊢  
  : , : , :
61instantiation79, 66, 67  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
63instantiation68, 69, 81  ⊢  
  : , : , :
64axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
65instantiation79, 71, 70  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
67instantiation79, 71, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
69instantiation73, 74  ⊢  
  : , :
70instantiation79, 75, 76  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
72instantiation77, 78  ⊢  
  :
73theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
77theorem  ⊢  
 proveit.numbers.negation.int_closure
78instantiation79, 80, 81  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
81assumption  ⊢  
*equality replacement requirements