logo

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  ⊢  
  : , :
1theorem  ⊢  
 proveit.logic.equality.equals_reversal
2instantiation3, 4, 5  ⊢  
  : , : , :
3axiom  ⊢  
 proveit.logic.equality.equals_transitivity
4instantiation6, 7  ⊢  
  : , : , :
5instantiation8, 45, 9, 25, 10*, 11*  ⊢  
  : , : , :
6axiom  ⊢  
 proveit.logic.equality.substitution
7instantiation12, 45, 20, 21  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.posnat_power_of_product
9instantiation13, 20, 14  ⊢  
  : , :
10instantiation15, 16, 17, 18  ⊢  
  : , : , : , :
11instantiation19, 20, 23, 49, 21, 22*  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.division.div_as_mult
13theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
14instantiation57, 48, 23  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
16instantiation24, 25, 45  ⊢  
  : , :
17instantiation26, 59, 27, 28, 29  ⊢  
  : , : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
19theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
20instantiation57, 48, 30  ⊢  
  : , : , :
21instantiation31, 32  ⊢  
  :
22instantiation33, 34, 45, 35*  ⊢  
  : , :
23instantiation57, 52, 36  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_nat_pos_expansion
25theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
26theorem  ⊢  
 proveit.core_expr_types.operations.operands_substitution_via_tuple
27instantiation37, 59  ⊢  
  : , :
28instantiation38  ⊢  
  : , :
29instantiation39  ⊢  
  :
30instantiation57, 40, 42  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
32instantiation57, 41, 42  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_left
34instantiation57, 48, 43  ⊢  
  : , : , :
35instantiation44, 45  ⊢  
  :
36instantiation57, 55, 46  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.core_expr_types.tuples.range_from1_len_typical_eq
38theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39theorem  ⊢  
 proveit.numbers.numerals.decimals.reduce_2_repeats
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
43instantiation57, 52, 47  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
45instantiation57, 48, 49  ⊢  
  : , : , :
46instantiation50, 51  ⊢  
  :
47instantiation57, 55, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49instantiation57, 52, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.negation.int_closure
51instantiation57, 58, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation57, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation57, 58, 59  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements