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	instantiation	5, 6	⊢
	:
2	instantiation	63, 53, 7	⊢
	: , : , :
3	instantiation	8, 9, 10, 11	⊢
	: , :
4	instantiation	12, 13	⊢
	:
5	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_neg_exp
6	instantiation	63, 14, 15	⊢
	: , : , :
7	instantiation	63, 58, 22	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.division.div_complex_closure
9	instantiation	16, 17, 18	⊢
	: , : , :
10	instantiation	63, 53, 19	⊢
	: , : , :
11	instantiation	20, 50	⊢
	:
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
13	instantiation	63, 21, 22	⊢
	: , : , :
14	instantiation	23, 24, 25	⊢
	: , :
15	assumption		⊢
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	44, 33, 26	⊢
	: , :
18	instantiation	27, 28, 29	⊢
	: , : , :
19	instantiation	63, 56, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
23	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
24	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
25	instantiation	31, 41, 32	⊢
	: , :
26	instantiation	44, 39, 40	⊢
	: , :
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	34, 51, 65, 35, 38, 36, 33, 39, 40	⊢
	: , : , : , : , : , :
29	instantiation	34, 35, 65, 36, 37, 38, 45, 46, 39, 40	⊢
	: , : , : , : , : , :
30	instantiation	63, 61, 41	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
32	instantiation	42, 43	⊢
	:
33	instantiation	44, 45, 46	⊢
	: , :
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	47	⊢
	: , :
38	instantiation	47	⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
40	instantiation	63, 53, 48	⊢
	: , : , :
41	instantiation	63, 49, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.negation.int_closure
43	instantiation	63, 64, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
45	instantiation	63, 53, 52	⊢
	: , : , :
46	instantiation	63, 53, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	instantiation	63, 56, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
50	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
52	instantiation	63, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
54	instantiation	63, 58, 59	⊢
	: , : , :
55	instantiation	63, 61, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	63, 61, 62	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat2