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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.ordering.less_is_not_eq
2instantiation5, 6, 7,  ⊢  
  : , :
3reference21  ⊢  
4instantiation8, 9,  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
6instantiation61, 29, 10,  ⊢  
  : , : , :
7instantiation11, 12  ⊢  
  :
8theorem  ⊢  
 proveit.numbers.addition.subtraction.neg_difference
9instantiation45, 13, 14,  ⊢  
  : , : , :
10instantiation61, 35, 15,  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.negation.real_closure
12instantiation16, 21, 22, 23  ⊢  
  : , : , :
13instantiation17, 18, 19,  ⊢  
  : , : , :
14instantiation20, 21, 22, 23  ⊢  
  : , : , :
15instantiation61, 24, 26,  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
17theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
18instantiation25, 31, 32, 26,  ⊢  
  : , : , :
19instantiation27, 28  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
22instantiation61, 29, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
24instantiation48, 31, 32  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
26assumption  ⊢  
27theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
28instantiation33, 34  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
30instantiation61, 35, 50  ⊢  
  : , : , :
31instantiation54, 36, 50  ⊢  
  : , :
32instantiation59, 37  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
34instantiation38, 39, 40  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36instantiation59, 55  ⊢  
  :
37instantiation54, 42, 50  ⊢  
  : , :
38theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
39instantiation41, 42, 43  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
41theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
42instantiation61, 44, 52  ⊢  
  : , : , :
43instantiation45, 46, 47  ⊢  
  : , : , :
44instantiation48, 50, 51  ⊢  
  : , :
45theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
46theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
47instantiation49, 50, 51, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
49theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
50instantiation61, 62, 53  ⊢  
  : , : , :
51instantiation54, 55, 56  ⊢  
  : , :
52assumption  ⊢  
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
55instantiation61, 57, 58  ⊢  
  : , : , :
56instantiation59, 60  ⊢  
  :
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
58theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
59theorem  ⊢  
 proveit.numbers.negation.int_closure
60instantiation61, 62, 63  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2