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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  ⊢  
  : , : , :
1reference28  ⊢  
2instantiation3, 4, 5, 6, 7*  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_as_mult
4instantiation78, 56, 8  ⊢  
  : , : , :
5instantiation78, 56, 9  ⊢  
  : , : , :
6instantiation24, 13  ⊢  
  :
7instantiation35, 10, 11  ⊢  
  : , : , :
8instantiation68, 69, 12  ⊢  
  : , : , :
9instantiation68, 69, 13  ⊢  
  : , : , :
10instantiation28, 14  ⊢  
  : , : , :
11instantiation15, 41, 16, 55, 19, 17*  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
13theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
14instantiation18, 41, 62, 57, 19, 20*  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
16instantiation21, 62, 57  ⊢  
  : , :
17instantiation35, 22, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
19instantiation24, 66  ⊢  
  :
20instantiation25, 48, 26, 27*  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
22instantiation28, 29  ⊢  
  : , : , :
23instantiation30, 31, 32, 33*  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
26instantiation78, 56, 64  ⊢  
  : , : , :
27instantiation34, 48  ⊢  
  :
28axiom  ⊢  
 proveit.logic.equality.substitution
29instantiation35, 36, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
31instantiation78, 38, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
33instantiation40, 41  ⊢  
  :
34theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
35axiom  ⊢  
 proveit.logic.equality.equals_transitivity
36instantiation42, 43, 73, 80, 44, 45, 48, 49, 46  ⊢  
  : , : , : , : , : , :
37instantiation47, 48, 49, 50  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
39instantiation78, 51, 52  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
41instantiation78, 56, 53  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.addition.disassociation
43axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
44theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45instantiation54  ⊢  
  : , :
46instantiation78, 56, 55  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
48instantiation78, 56, 62  ⊢  
  : , : , :
49instantiation78, 56, 57  ⊢  
  : , : , :
50instantiation58  ⊢  
  :
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
52instantiation78, 59, 60  ⊢  
  : , : , :
53instantiation78, 71, 61  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
55instantiation63, 62  ⊢  
  :
56theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
57instantiation63, 64  ⊢  
  :
58axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
59theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
60instantiation78, 65, 66  ⊢  
  : , : , :
61instantiation78, 76, 67  ⊢  
  : , : , :
62instantiation68, 69, 70  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.negation.real_closure
64instantiation78, 71, 72  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
67instantiation78, 79, 73  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
69instantiation74, 75  ⊢  
  : , :
70axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
71theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
72instantiation78, 76, 77  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
74theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
75theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
76theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
77instantiation78, 79, 80  ⊢  
  : , : , :
78theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
80theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements