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