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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
0generalization1  ⊢  
1instantiation2, 58, 3, 4,  ⊢  
  : , :
2theorem  ⊢  
 proveit.numbers.division.div_real_closure
3instantiation5, 15, 75,  ⊢  
  : , :
4instantiation6, 7,  ⊢  
  :
5theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
6theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
7instantiation73, 8, 9,  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
9instantiation10, 15, 11,  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
11instantiation12, 13,  ⊢  
  : , :
12theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
13instantiation14, 36, 15, 16,  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq
15instantiation17, 18, 19,  ⊢  
  : , :
16instantiation20, 21,  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
18instantiation73, 61, 22,  ⊢  
  : , : , :
19instantiation23, 24  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
21instantiation25, 26, 27,  ⊢  
  : , : , :
22instantiation73, 66, 28,  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.negation.real_closure
24instantiation29, 36, 58, 31  ⊢  
  : , : , :
25axiom  ⊢  
 proveit.numbers.ordering.transitivity_less_less
26instantiation30, 36, 58, 31  ⊢  
  : , : , :
27instantiation43, 32, 33,  ⊢  
  : , : , :
28instantiation73, 34, 40,  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
31theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
32instantiation35, 58, 36, 37, 38, 39*  ⊢  
  : , : , :
33instantiation50, 41, 64, 40,  ⊢  
  : , : , :
34instantiation59, 41, 64  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
37instantiation73, 61, 42  ⊢  
  : , : , :
38instantiation43, 44, 45  ⊢  
  : , : , :
39instantiation46, 47, 48  ⊢  
  : , : , :
40assumption  ⊢  
41instantiation63, 49, 67  ⊢  
  : , :
42instantiation73, 66, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
44theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
45instantiation50, 67, 60, 56  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
47instantiation51, 53  ⊢  
  :
48instantiation52, 53, 54  ⊢  
  : , :
49instantiation73, 55, 56  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
51theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
52theorem  ⊢  
 proveit.numbers.addition.commutation
53instantiation73, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
55instantiation59, 67, 60  ⊢  
  : , :
56assumption  ⊢  
57theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
58instantiation73, 61, 62  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
60instantiation63, 64, 65  ⊢  
  : , :
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
62instantiation73, 66, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
64instantiation73, 68, 69  ⊢  
  : , : , :
65instantiation70, 71  ⊢  
  :
66theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
67instantiation73, 74, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
69theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
70theorem  ⊢  
 proveit.numbers.negation.int_closure
71instantiation73, 74, 75  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
73theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements