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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  ⊢  
  : , : , :
1reference29  ⊢  
2instantiation29, 4, 5  ⊢  
  : , : , :
3instantiation29, 6, 7  ⊢  
  : , : , :
4instantiation37, 8  ⊢  
  : , : , :
5instantiation37, 9  ⊢  
  : , : , :
6instantiation10, 11, 80, 12, 13, 14, 15, 17, 22  ⊢  
  : , : , : , : , : , :
7instantiation16, 22, 17, 18  ⊢  
  : , : , :
8instantiation37, 19  ⊢  
  : , : , :
9instantiation37, 19  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.addition.disassociation
11theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
12axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
13instantiation20  ⊢  
  : , :
14theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15instantiation21, 22  ⊢  
  :
16theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_31
17instantiation78, 61, 23  ⊢  
  : , : , :
18instantiation24  ⊢  
  :
19instantiation25, 40, 54, 50, 26*  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21theorem  ⊢  
 proveit.numbers.negation.complex_closure
22instantiation78, 61, 27  ⊢  
  : , : , :
23instantiation42, 28  ⊢  
  :
24axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
25theorem  ⊢  
 proveit.numbers.division.div_as_mult
26instantiation29, 30, 31  ⊢  
  : , : , :
27instantiation32, 47, 49  ⊢  
  : , :
28instantiation33, 34, 35, 36  ⊢  
  : , : , :
29axiom  ⊢  
 proveit.logic.equality.equals_transitivity
30instantiation37, 38  ⊢  
  : , : , :
31instantiation39, 40, 41  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
34instantiation42, 43  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
36assumption  ⊢  
37axiom  ⊢  
 proveit.logic.equality.substitution
38instantiation44, 45, 75, 46*  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.multiplication.commutation
40instantiation78, 61, 49  ⊢  
  : , : , :
41instantiation78, 61, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.negation.real_closure
43instantiation48, 49, 62, 50  ⊢  
  : , :
44theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
45instantiation78, 51, 52  ⊢  
  : , : , :
46instantiation53, 54  ⊢  
  :
47instantiation78, 67, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.division.div_real_closure
49instantiation78, 56, 57  ⊢  
  : , : , :
50instantiation58, 77  ⊢  
  :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
52instantiation78, 59, 60  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
54instantiation78, 61, 62  ⊢  
  : , : , :
55instantiation78, 63, 64  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
58theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
60instantiation78, 65, 66  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
62instantiation78, 67, 68  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
64instantiation69, 70, 71  ⊢  
  : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
66instantiation78, 72, 77  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
68instantiation78, 73, 74  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
70instantiation78, 76, 75  ⊢  
  : , : , :
71instantiation78, 76, 77  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
73theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
74instantiation78, 79, 80  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
76theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
77theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
78theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
80theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements