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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
0modus ponens1, 2  ⊢  
1instantiation3  ⊢  
  : , : , :
2generalization4  ⊢  
3theorem  ⊢  
 proveit.numbers.summation.summation_real_closure
4instantiation5, 35, 6, 7,  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.division.div_real_closure
6instantiation8, 16, 76,  ⊢  
  : , :
7instantiation9, 10,  ⊢  
  :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
10instantiation74, 11, 12,  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
12instantiation13, 16, 14,  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
14instantiation15, 16, 34, 17,  ⊢  
  : , :
15theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq
16instantiation18, 19, 20,  ⊢  
  : , :
17instantiation21, 22,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
19instantiation74, 42, 23,  ⊢  
  : , : , :
20instantiation24, 25  ⊢  
  :
21theorem  ⊢  
 proveit.numbers.addition.subtraction.neg_difference
22instantiation58, 26, 27,  ⊢  
  : , : , :
23instantiation74, 48, 28,  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.negation.real_closure
25instantiation29, 34, 35, 36  ⊢  
  : , : , :
26instantiation30, 31, 32,  ⊢  
  : , : , :
27instantiation33, 34, 35, 36  ⊢  
  : , : , :
28instantiation74, 37, 39,  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
30theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
31instantiation38, 44, 45, 39,  ⊢  
  : , : , :
32instantiation40, 41  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
35instantiation74, 42, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
37instantiation61, 44, 45  ⊢  
  : , :
38theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
39assumption  ⊢  
40theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
41instantiation46, 47  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation74, 48, 63  ⊢  
  : , : , :
44instantiation67, 49, 63  ⊢  
  : , :
45instantiation72, 50  ⊢  
  :
46theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
47instantiation51, 52, 53  ⊢  
  : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
49instantiation72, 68  ⊢  
  :
50instantiation67, 55, 63  ⊢  
  : , :
51theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
52instantiation54, 55, 56  ⊢  
  :
53theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
54theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
55instantiation74, 57, 65  ⊢  
  : , : , :
56instantiation58, 59, 60  ⊢  
  : , : , :
57instantiation61, 63, 64  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
59theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
60instantiation62, 63, 64, 65  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
62theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
63instantiation74, 75, 66  ⊢  
  : , : , :
64instantiation67, 68, 69  ⊢  
  : , :
65assumption  ⊢  
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
67theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
68instantiation74, 70, 71  ⊢  
  : , : , :
69instantiation72, 73  ⊢  
  :
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
71theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
72theorem  ⊢  
 proveit.numbers.negation.int_closure
73instantiation74, 75, 76  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2