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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
0modus ponens1, 2  ⊢  
1instantiation3  ⊢  
  : , : , :
2generalization4  ⊢  
3theorem  ⊢  
 proveit.numbers.summation.summation_real_closure
4instantiation5, 6, 7, 8,  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.division.div_real_closure
6instantiation62, 18, 9  ⊢  
  : , : , :
7instantiation10, 16, 64,  ⊢  
  : , :
8instantiation11, 12,  ⊢  
  :
9instantiation62, 23, 51  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
12instantiation62, 13, 14,  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
14instantiation15, 16, 17,  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
16instantiation62, 18, 19,  ⊢  
  : , : , :
17instantiation20, 24, 21, 22,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
19instantiation62, 23, 24,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
21theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
22instantiation25, 26, 27,  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
24instantiation62, 28, 30,  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
26instantiation29, 33, 34, 30,  ⊢  
  : , : , :
27instantiation31, 32  ⊢  
  :
28instantiation49, 33, 34  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
32instantiation35, 36  ⊢  
  :
33instantiation55, 37, 51  ⊢  
  : , :
34instantiation60, 38  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
36instantiation39, 40, 41  ⊢  
  : , :
37instantiation60, 56  ⊢  
  :
38instantiation55, 43, 51  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
40instantiation42, 43, 44  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
42theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
43instantiation62, 45, 53  ⊢  
  : , : , :
44instantiation46, 47, 48  ⊢  
  : , : , :
45instantiation49, 51, 52  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
47theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
48instantiation50, 51, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
50theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
51instantiation62, 63, 54  ⊢  
  : , : , :
52instantiation55, 56, 57  ⊢  
  : , :
53assumption  ⊢  
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