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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  ⊢  
  : , : , :
1reference64  ⊢  
2theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
3modus ponens4, 5  ⊢  
4instantiation6  ⊢  
  : , : , :
5generalization7  ⊢  
6theorem  ⊢  
 proveit.numbers.summation.summation_real_closure
7instantiation8, 9, 10, 11,  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.division.div_real_closure
9instantiation64, 18, 12  ⊢  
  : , : , :
10instantiation13, 14, 66,  ⊢  
  : , :
11instantiation15, 16, 17,  ⊢  
  : , :
12instantiation64, 23, 53  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
14instantiation64, 18, 19,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
16instantiation64, 21, 20,  ⊢  
  : , : , :
17instantiation64, 21, 22  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
19instantiation64, 23, 27,  ⊢  
  : , : , :
20instantiation64, 25, 24,  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
22instantiation64, 25, 26  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
24instantiation40, 27, 28,  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
26theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
27instantiation64, 29, 36,  ⊢  
  : , : , :
28instantiation46, 30, 31,  ⊢  
  : , : , :
29instantiation51, 34, 35  ⊢  
  : , :
30instantiation32, 33  ⊢  
  :
31instantiation52, 34, 35, 36,  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
33instantiation37, 38, 50  ⊢  
  : , :
34instantiation57, 41, 53  ⊢  
  : , :
35instantiation57, 58, 39  ⊢  
  : , :
36assumption  ⊢  
37theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
38instantiation40, 41, 42  ⊢  
  :
39instantiation64, 43, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
41instantiation64, 45, 55  ⊢  
  : , : , :
42instantiation46, 47, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
44instantiation49, 50  ⊢  
  :
45instantiation51, 53, 54  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
47theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
48instantiation52, 53, 54, 55  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
50theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
51theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
52theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
53instantiation64, 65, 56  ⊢  
  : , : , :
54instantiation57, 58, 59  ⊢  
  : , :
55assumption  ⊢  
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
57theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
58instantiation64, 60, 61  ⊢  
  : , : , :
59instantiation62, 63  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
61theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
62theorem  ⊢  
 proveit.numbers.negation.int_closure
63instantiation64, 65, 66  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2