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 type	requirements	statement
0	instantiation	1, 2	, , ⊢
	: , : , :
1	reference	5	⊢
2	instantiation	26, 3, 4	, , ⊢
	: , : , :
3	instantiation	5, 6	, ⊢
	: , : , :
4	instantiation	7, 11, 8, 9	, , ⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	10, 11, 13, 14	, ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.complex_power_of_complex_power
8	instantiation	12, 13, 14	, ⊢
	: , :
9	instantiation	59, 49, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
12	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
13	instantiation	18, 16, 17	⊢
	: , : , :
14	instantiation	18, 19, 20	⊢
	: , : , :
15	instantiation	59, 53, 21	⊢
	: , : , :
16	instantiation	42, 33, 22	⊢
	: , :
17	instantiation	26, 23, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	42, 33, 25	⊢
	: , :
20	instantiation	26, 27, 28	⊢
	: , : , :
21	instantiation	59, 57, 29	⊢
	: , : , :
22	instantiation	42, 39, 31	⊢
	: , :
23	instantiation	34, 32, 61, 35, 30, 36, 33, 39, 31	⊢
	: , : , : , : , : , :
24	instantiation	34, 35, 61, 36, 37, 30, 43, 44, 39, 31	⊢
	: , : , : , : , : , :
25	instantiation	42, 39, 40	⊢
	: , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	34, 32, 61, 35, 38, 36, 33, 39, 40	⊢
	: , : , : , : , : , :
28	instantiation	34, 35, 61, 36, 37, 38, 43, 44, 39, 40	⊢
	: , : , : , : , : , :
29	assumption		⊢
30	instantiation	45	⊢
	: , :
31	instantiation	59, 49, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
33	instantiation	42, 43, 44	⊢
	: , :
34	theorem		⊢
	proveit.numbers.multiplication.disassociation
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37	instantiation	45	⊢
	: , :
38	instantiation	45	⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
40	instantiation	59, 49, 46	⊢
	: , : , :
41	instantiation	59, 53, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
43	instantiation	59, 49, 48	⊢
	: , : , :
44	instantiation	59, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	59, 55, 51	⊢
	: , : , :
47	instantiation	59, 57, 52	⊢
	: , : , :
48	instantiation	59, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	59, 55, 56	⊢
	: , : , :
51	assumption		⊢
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	59, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	59, 60, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2