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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*, 6*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.posnat_power_of_product
2reference17  ⊢  
3instantiation58, 28, 7  ⊢  
  : , : , :
4reference16  ⊢  
5instantiation8, 9, 10, 11  ⊢  
  : , : , : , :
6instantiation12, 29  ⊢  
  :
7instantiation58, 13, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
9instantiation15, 16, 17  ⊢  
  : , :
10instantiation18, 41, 19, 20, 21  ⊢  
  : , : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
12theorem  ⊢  
 proveit.numbers.exponentiation.square_abs_real_simp
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
14instantiation22, 23  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_nat_pos_expansion
16theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
17instantiation58, 28, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.core_expr_types.operations.operands_substitution_via_tuple
19instantiation25, 41  ⊢  
  : , :
20instantiation26  ⊢  
  : , :
21instantiation27  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.absolute_value.abs_complex_closure
23instantiation58, 28, 29  ⊢  
  : , : , :
24instantiation58, 43, 30  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.core_expr_types.tuples.range_from1_len_typical_eq
26theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27theorem  ⊢  
 proveit.numbers.numerals.decimals.reduce_2_repeats
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation31, 32, 33  ⊢  
  : , :
30instantiation58, 45, 34  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
32instantiation35, 36, 37, 38  ⊢  
  : , : , :
33instantiation39, 40  ⊢  
  :
34instantiation58, 56, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
37instantiation58, 43, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
39theorem  ⊢  
 proveit.numbers.negation.real_closure
40instantiation58, 43, 44  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
42instantiation58, 45, 53  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
44instantiation58, 45, 46  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation58, 47, 48  ⊢  
  : , : , :
47instantiation49, 50, 55  ⊢  
  : , :
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
50instantiation51, 52, 53  ⊢  
  : , :
51theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
52instantiation54, 55  ⊢  
  :
53instantiation58, 56, 57  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.negation.int_closure
55instantiation58, 59, 60  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
60theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements