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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  ⊢  
  : , : , :
1reference18  ⊢  
2instantiation3, 35, 4, 5, 6*  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_as_mult
4instantiation70, 50, 7  ⊢  
  : , : , :
5instantiation8, 9, 10  ⊢  
  : , :
6instantiation11, 12, 13  ⊢  
  : , : , :
7instantiation14, 37, 72  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
9instantiation70, 16, 15  ⊢  
  : , : , :
10instantiation70, 16, 17  ⊢  
  : , : , :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation18, 19  ⊢  
  : , : , :
13instantiation20, 21  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
15instantiation70, 22, 33  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
17instantiation70, 22, 23  ⊢  
  : , : , :
18axiom  ⊢  
 proveit.logic.equality.substitution
19instantiation24, 29, 51, 25, 26, 27*  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
21instantiation28, 29, 30  ⊢  
  : , :
22theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
23theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
24theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
25instantiation31, 41  ⊢  
  :
26instantiation32, 33  ⊢  
  :
27instantiation34, 43, 35, 36*  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
29instantiation70, 50, 37  ⊢  
  : , : , :
30instantiation70, 50, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.negation.real_closure
32theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
33instantiation39, 52, 40  ⊢  
  :
34theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
35instantiation70, 50, 41  ⊢  
  : , : , :
36instantiation42, 43  ⊢  
  :
37instantiation70, 54, 44  ⊢  
  : , : , :
38instantiation70, 54, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
40instantiation46, 47, 48  ⊢  
  : , : , :
41instantiation70, 54, 49  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
43instantiation70, 50, 51  ⊢  
  : , : , :
44instantiation70, 58, 52  ⊢  
  : , : , :
45instantiation70, 58, 65  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
47theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
48instantiation53, 60, 61, 57  ⊢  
  : , : , :
49instantiation70, 58, 60  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
51instantiation70, 54, 55  ⊢  
  : , : , :
52instantiation70, 56, 57  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
55instantiation70, 58, 69  ⊢  
  : , : , :
56instantiation59, 60, 61  ⊢  
  : , :
57assumption  ⊢  
58theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
59theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
60instantiation70, 71, 62  ⊢  
  : , : , :
61instantiation63, 64, 65  ⊢  
  : , :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
63theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
64instantiation70, 66, 67  ⊢  
  : , : , :
65instantiation68, 69  ⊢  
  :
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
67theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
68theorem  ⊢  
 proveit.numbers.negation.int_closure
69instantiation70, 71, 72  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
72theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements