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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.sets.inclusion.fold_subset_eq
2generalization3  ⊢  
3instantiation4, 5, 6,  ⊢  
  :
4theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
5instantiation7, 13, 14, 15,  ⊢  
  : , : , :
6instantiation24, 8, 9,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
8instantiation10, 11  ⊢  
  : , :
9instantiation12, 13, 14, 15,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
11instantiation16, 40, 17, 18, 19, 20*  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_cc_lower_bound
13instantiation62, 44, 21  ⊢  
  : , : , :
14instantiation62, 44, 22  ⊢  
  : , : , :
15assumption  ⊢  
16theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
17theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
18instantiation62, 44, 23  ⊢  
  : , : , :
19instantiation24, 25, 26  ⊢  
  : , : , :
20instantiation27, 28, 29  ⊢  
  : , : , :
21instantiation62, 50, 30  ⊢  
  : , : , :
22instantiation62, 50, 31  ⊢  
  : , : , :
23instantiation62, 50, 41  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
25theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
26instantiation32, 52, 53, 47  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
28instantiation33, 35  ⊢  
  :
29instantiation34, 35, 36  ⊢  
  : , :
30instantiation55, 37, 38  ⊢  
  : , :
31instantiation55, 56, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
33theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
34theorem  ⊢  
 proveit.numbers.addition.commutation
35instantiation62, 39, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
37instantiation55, 41, 52  ⊢  
  : , :
38instantiation62, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation62, 44, 45  ⊢  
  : , : , :
41instantiation62, 46, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
43instantiation48, 49  ⊢  
  :
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
45instantiation62, 50, 52  ⊢  
  : , : , :
46instantiation51, 52, 53  ⊢  
  : , :
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
52instantiation62, 63, 54  ⊢  
  : , : , :
53instantiation55, 56, 57  ⊢  
  : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
56instantiation62, 58, 59  ⊢  
  : , : , :
57instantiation60, 61  ⊢  
  :
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
59theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
60theorem  ⊢  
 proveit.numbers.negation.int_closure
61instantiation62, 63, 64  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
64theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements