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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, 4, 5*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_as_mult
2reference34  ⊢  
3instantiation69, 49, 6  ⊢  
  : , : , :
4instantiation7, 8, 9  ⊢  
  : , :
5instantiation10, 11, 12  ⊢  
  : , : , :
6instantiation13, 36, 71  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
8instantiation69, 15, 14  ⊢  
  : , : , :
9instantiation69, 15, 16  ⊢  
  : , : , :
10axiom  ⊢  
 proveit.logic.equality.equals_transitivity
11instantiation17, 18  ⊢  
  : , : , :
12instantiation19, 20  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
14instantiation69, 21, 32  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
16instantiation69, 21, 22  ⊢  
  : , : , :
17axiom  ⊢  
 proveit.logic.equality.substitution
18instantiation23, 28, 50, 24, 25, 26*  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
20instantiation27, 28, 29  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
22theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
23theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
24instantiation30, 40  ⊢  
  :
25instantiation31, 32  ⊢  
  :
26instantiation33, 42, 34, 35*  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
28instantiation69, 49, 36  ⊢  
  : , : , :
29instantiation69, 49, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.negation.real_closure
31theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
32instantiation38, 51, 39  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
34instantiation69, 49, 40  ⊢  
  : , : , :
35instantiation41, 42  ⊢  
  :
36instantiation69, 53, 43  ⊢  
  : , : , :
37instantiation69, 53, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
39instantiation45, 46, 47  ⊢  
  : , : , :
40instantiation69, 53, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
42instantiation69, 49, 50  ⊢  
  : , : , :
43instantiation69, 57, 51  ⊢  
  : , : , :
44instantiation69, 57, 64  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
46theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
47instantiation52, 59, 60, 56  ⊢  
  : , : , :
48instantiation69, 57, 59  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation69, 53, 54  ⊢  
  : , : , :
51instantiation69, 55, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
54instantiation69, 57, 68  ⊢  
  : , : , :
55instantiation58, 59, 60  ⊢  
  : , :
56assumption  ⊢  
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
58theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
59instantiation69, 70, 61  ⊢  
  : , : , :
60instantiation62, 63, 64  ⊢  
  : , :
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
62theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
63instantiation69, 65, 66  ⊢  
  : , : , :
64instantiation67, 68  ⊢  
  :
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
66theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
67theorem  ⊢  
 proveit.numbers.negation.int_closure
68instantiation69, 70, 71  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements