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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*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
2reference11  ⊢  
3instantiation52, 22, 5  ⊢  
  : , : , :
4instantiation6, 7, 8  ⊢  
  : , : , :
5instantiation9, 21, 23  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation10, 51, 14, 13, 16, 15, 11, 17, 18  ⊢  
  : , : , : , : , : , :
8instantiation12, 13, 14, 15, 16, 17, 18  ⊢  
  : , : , : , :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11instantiation52, 22, 19  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
13axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
14theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
15theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16instantiation20  ⊢  
  : , :
17instantiation52, 22, 21  ⊢  
  : , : , :
18instantiation52, 22, 23  ⊢  
  : , : , :
19instantiation52, 26, 24  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21instantiation52, 26, 25  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
23instantiation52, 26, 27  ⊢  
  : , : , :
24instantiation52, 28, 44  ⊢  
  : , : , :
25instantiation52, 28, 29  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
27instantiation52, 30, 31  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
29instantiation52, 32, 33  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
31instantiation34, 35, 36  ⊢  
  : , :
32instantiation37, 38, 49  ⊢  
  : , :
33assumption  ⊢  
34theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
35instantiation52, 39, 40  ⊢  
  : , : , :
36instantiation48, 41  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
38instantiation42, 43, 44  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
40instantiation52, 45, 46  ⊢  
  : , : , :
41instantiation52, 53, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
43instantiation48, 49  ⊢  
  :
44instantiation52, 50, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
47axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
48theorem  ⊢  
 proveit.numbers.negation.int_closure
49instantiation52, 53, 54  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements