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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,  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_not_in_interval_cc
2reference49  ⊢  
3reference26  ⊢  
4reference45  ⊢  
5instantiation6, 7, 17,  ⊢  
  : , :
6theorem  ⊢  
 proveit.logic.booleans.disjunction.or_if_only_right
7instantiation8, 49, 45, 9,  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.ordering.not_less_from_less_eq
9instantiation10, 44, 26, 11, 12, 13*, 14*,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
11instantiation15, 45, 51  ⊢  
  : , :
12instantiation16, 26, 45, 51, 17, 18,  ⊢  
  : , : , :
13instantiation19, 42, 41, 20, 21  ⊢  
  : , : , :
14instantiation22, 23, 24  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
16theorem  ⊢  
 proveit.numbers.ordering.less_add_right_weak
17assumption  ⊢  
18instantiation25, 62  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add
20instantiation60, 48, 26  ⊢  
  : , : , :
21instantiation27, 28, 29  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.logic.equality.equals_transitivity
23instantiation30, 31, 32, 59, 33, 34, 37, 41, 35  ⊢  
  : , : , : , : , : , :
24instantiation36, 41, 37, 38  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_lower_bound
26instantiation60, 54, 39  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
28theorem  ⊢  
 proveit.numbers.numerals.decimals.add_5_1
29instantiation40, 41, 42  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.addition.disassociation
31axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
33theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34instantiation43  ⊢  
  : , :
35instantiation60, 48, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
37instantiation60, 48, 45  ⊢  
  : , : , :
38instantiation46  ⊢  
  :
39instantiation60, 57, 47  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.addition.commutation
41instantiation60, 48, 51  ⊢  
  : , : , :
42instantiation60, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44instantiation50, 51  ⊢  
  :
45assumption  ⊢  
46axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
47instantiation60, 61, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49instantiation60, 54, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.negation.real_closure
51instantiation60, 54, 55  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat6
53instantiation60, 57, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
55instantiation60, 57, 58  ⊢  
  : , : , :
56instantiation60, 61, 59  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
58instantiation60, 61, 62  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
*equality replacement requirements