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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  ⊢  
  : , : , :
1reference19  ⊢  
2instantiation12, 4  ⊢  
  : , : , :
3instantiation19, 5, 6  ⊢  
  : , : , :
4instantiation7, 73, 76, 29, 8, 31, 33, 32, 34  ⊢  
  : , : , : , : , : , :
5instantiation19, 9, 10  ⊢  
  : , : , :
6instantiation11, 17  ⊢  
  :
7theorem  ⊢  
 proveit.numbers.multiplication.disassociation
8instantiation39  ⊢  
  : , :
9instantiation12, 13  ⊢  
  : , : , :
10instantiation14, 15, 16, 17, 18*  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.division.frac_one_denom
12axiom  ⊢  
 proveit.logic.equality.substitution
13instantiation19, 20, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
15instantiation74, 23, 22  ⊢  
  : , : , :
16instantiation74, 23, 24  ⊢  
  : , : , :
17instantiation74, 52, 25  ⊢  
  : , : , :
18instantiation26, 32  ⊢  
  :
19axiom  ⊢  
 proveit.logic.equality.equals_transitivity
20instantiation27, 29, 73, 31, 33, 32, 34  ⊢  
  : , : , : , : , : , : , :
21instantiation28, 73, 76, 29, 30, 31, 32, 33, 34  ⊢  
  : , : , : , : , : , :
22instantiation74, 35, 45  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
24instantiation74, 36, 37  ⊢  
  : , : , :
25instantiation38, 63, 41  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
27theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
28theorem  ⊢  
 proveit.numbers.multiplication.association
29axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
30instantiation39  ⊢  
  : , :
31theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32instantiation74, 52, 40  ⊢  
  : , : , :
33instantiation74, 52, 63  ⊢  
  : , : , :
34instantiation74, 52, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
37instantiation74, 42, 43  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40instantiation74, 44, 45  ⊢  
  : , : , :
41instantiation74, 46, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43instantiation74, 48, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
47instantiation50, 51  ⊢  
  :
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
50theorem  ⊢  
 proveit.numbers.absolute_value.abs_complex_closure
51instantiation74, 52, 53  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
53instantiation54, 55, 58, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
55instantiation57, 58  ⊢  
  :
56instantiation59, 60  ⊢  
  :
57theorem  ⊢  
 proveit.numbers.negation.real_closure
58instantiation61, 62, 63, 64  ⊢  
  : , :
59theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
60assumption  ⊢  
61theorem  ⊢  
 proveit.numbers.division.div_real_closure
62instantiation74, 66, 65  ⊢  
  : , : , :
63instantiation74, 66, 67  ⊢  
  : , : , :
64instantiation68, 69  ⊢  
  :
65instantiation74, 71, 70  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
67instantiation74, 71, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
69theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
70instantiation74, 75, 73  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
72instantiation74, 75, 76  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
74theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements