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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  ⊢  
  : , : , :
1reference15  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7  ⊢  
  :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation8, 12, 27, 28, 9, 10*  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
7instantiation11, 12, 13  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
9instantiation14, 69  ⊢  
  :
10instantiation15, 16, 17  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
12instantiation67, 42, 18  ⊢  
  : , : , :
13instantiation19, 20  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
15axiom  ⊢  
 proveit.logic.equality.equals_transitivity
16instantiation21, 31, 44, 62, 33, 32, 34, 35, 22  ⊢  
  : , : , : , : , : , :
17instantiation23, 44, 31, 32, 33, 34, 35, 24, 25*  ⊢  
  : , : , : , : , :
18instantiation67, 48, 26  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.negation.complex_closure
20instantiation67, 42, 27  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.disassociation
22instantiation67, 42, 28  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
24instantiation67, 42, 29  ⊢  
  : , : , :
25instantiation30, 44, 31, 32, 33, 34, 35  ⊢  
  : , : , : , :
26instantiation67, 47, 36  ⊢  
  : , : , :
27instantiation67, 48, 37  ⊢  
  : , : , :
28instantiation67, 48, 38  ⊢  
  : , : , :
29instantiation67, 48, 39  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
31axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
32instantiation40  ⊢  
  : , :
33theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34instantiation67, 42, 41  ⊢  
  : , : , :
35instantiation67, 42, 43  ⊢  
  : , : , :
36instantiation67, 61, 44  ⊢  
  : , : , :
37instantiation67, 56, 45  ⊢  
  : , : , :
38instantiation67, 47, 46  ⊢  
  : , : , :
39instantiation67, 47, 55  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41instantiation67, 48, 49  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation50, 51, 60  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
45instantiation52, 57, 53  ⊢  
  : , :
46instantiation54, 55  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
49instantiation67, 56, 57  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
51instantiation58, 59  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
53instantiation67, 68, 60  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.negation.int_closure
55instantiation67, 61, 62  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57instantiation63, 64, 65  ⊢  
  : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
63theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
64instantiation67, 68, 66  ⊢  
  : , : , :
65instantiation67, 68, 69  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
67theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
69theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements