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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,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_real_closure
2instantiation58, 14, 5  ⊢  
  : , : , :
3instantiation6, 12, 60,  ⊢  
  : , :
4instantiation7, 8,  ⊢  
  :
5instantiation58, 19, 47  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
8instantiation58, 9, 10,  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
10instantiation11, 12, 13,  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
12instantiation58, 14, 15,  ⊢  
  : , : , :
13instantiation16, 20, 17, 18,  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
15instantiation58, 19, 20,  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
17theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
18instantiation21, 22, 23,  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
20instantiation58, 24, 26,  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
22instantiation25, 29, 30, 26,  ⊢  
  : , : , :
23instantiation27, 28  ⊢  
  :
24instantiation45, 29, 30  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
26assumption  ⊢  
27theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
28instantiation31, 32  ⊢  
  :
29instantiation51, 33, 47  ⊢  
  : , :
30instantiation56, 34  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
32instantiation35, 36, 37  ⊢  
  : , :
33instantiation56, 52  ⊢  
  :
34instantiation51, 39, 47  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
36instantiation38, 39, 40  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
38theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
39instantiation58, 41, 49  ⊢  
  : , : , :
40instantiation42, 43, 44  ⊢  
  : , : , :
41instantiation45, 47, 48  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
43theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
44instantiation46, 47, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
46theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
47instantiation58, 59, 50  ⊢  
  : , : , :
48instantiation51, 52, 53  ⊢  
  : , :
49assumption  ⊢  
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
51theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
52instantiation58, 54, 55  ⊢  
  : , : , :
53instantiation56, 57  ⊢  
  :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
55theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
56theorem  ⊢  
 proveit.numbers.negation.int_closure
57instantiation58, 59, 60  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2