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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
2instantiation57, 11, 5  ⊢  
  : , : , :
3instantiation6, 7, 59,  ⊢  
  : , :
4instantiation8, 9, 10,  ⊢  
  : , :
5instantiation57, 16, 46  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
7instantiation57, 11, 12,  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
9instantiation57, 14, 13,  ⊢  
  : , : , :
10instantiation57, 14, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
12instantiation57, 16, 20,  ⊢  
  : , : , :
13instantiation57, 18, 17,  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
15instantiation57, 18, 19  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
17instantiation33, 20, 21,  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
19theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
20instantiation57, 22, 29,  ⊢  
  : , : , :
21instantiation39, 23, 24,  ⊢  
  : , : , :
22instantiation44, 27, 28  ⊢  
  : , :
23instantiation25, 26  ⊢  
  :
24instantiation45, 27, 28, 29,  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
26instantiation30, 31, 43  ⊢  
  : , :
27instantiation50, 34, 46  ⊢  
  : , :
28instantiation50, 51, 32  ⊢  
  : , :
29assumption  ⊢  
30theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
31instantiation33, 34, 35  ⊢  
  :
32instantiation57, 36, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
34instantiation57, 38, 48  ⊢  
  : , : , :
35instantiation39, 40, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
37instantiation42, 43  ⊢  
  :
38instantiation44, 46, 47  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
40theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
41instantiation45, 46, 47, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
44theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
45theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
46instantiation57, 58, 49  ⊢  
  : , : , :
47instantiation50, 51, 52  ⊢  
  : , :
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
50theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
51instantiation57, 53, 54  ⊢  
  : , : , :
52instantiation55, 56  ⊢  
  :
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
55theorem  ⊢  
 proveit.numbers.negation.int_closure
56instantiation57, 58, 59  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2