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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.equality.equals_reversal
2instantiation19, 3  ⊢  
  : , : , :
3instantiation4, 36, 5, 6, 7*  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_as_mult
5instantiation71, 51, 8  ⊢  
  : , : , :
6instantiation9, 10, 11  ⊢  
  : , :
7instantiation12, 13, 14  ⊢  
  : , : , :
8instantiation15, 38, 73  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
10instantiation71, 17, 16  ⊢  
  : , : , :
11instantiation71, 17, 18  ⊢  
  : , : , :
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation19, 20  ⊢  
  : , : , :
14instantiation21, 22  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
16instantiation71, 23, 34  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
18instantiation71, 23, 24  ⊢  
  : , : , :
19axiom  ⊢  
 proveit.logic.equality.substitution
20instantiation25, 30, 52, 26, 27, 28*  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
22instantiation29, 30, 31  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
24theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
25theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
26instantiation32, 42  ⊢  
  :
27instantiation33, 34  ⊢  
  :
28instantiation35, 44, 36, 37*  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
30instantiation71, 51, 38  ⊢  
  : , : , :
31instantiation71, 51, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.negation.real_closure
33theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34instantiation40, 53, 41  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
36instantiation71, 51, 42  ⊢  
  : , : , :
37instantiation43, 44  ⊢  
  :
38instantiation71, 55, 45  ⊢  
  : , : , :
39instantiation71, 55, 46  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
41instantiation47, 48, 49  ⊢  
  : , : , :
42instantiation71, 55, 50  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
44instantiation71, 51, 52  ⊢  
  : , : , :
45instantiation71, 59, 53  ⊢  
  : , : , :
46instantiation71, 59, 66  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
48theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
49instantiation54, 61, 62, 58  ⊢  
  : , : , :
50instantiation71, 59, 61  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52instantiation71, 55, 56  ⊢  
  : , : , :
53instantiation71, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
56instantiation71, 59, 70  ⊢  
  : , : , :
57instantiation60, 61, 62  ⊢  
  : , :
58assumption  ⊢  
59theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
60theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
61instantiation71, 72, 63  ⊢  
  : , : , :
62instantiation64, 65, 66  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
64theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
65instantiation71, 67, 68  ⊢  
  : , : , :
66instantiation69, 70  ⊢  
  :
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
68theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
69theorem  ⊢  
 proveit.numbers.negation.int_closure
70instantiation71, 72, 73  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements