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	⊢
	: , :
1	theorem		⊢
	proveit.numbers.addition.commutation
2	instantiation	4, 5	⊢
	:
3	instantiation	15, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.negation.complex_closure
5	instantiation	8, 9, 10, 11	⊢
	: , :
6	instantiation	38, 29, 12	⊢
	: , :
7	instantiation	23, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.division.div_complex_closure
9	instantiation	15, 16, 17	⊢
	: , : , :
10	instantiation	56, 46, 18	⊢
	: , : , :
11	instantiation	19, 44	⊢
	:
12	instantiation	38, 35, 21	⊢
	: , :
13	instantiation	30, 28, 58, 31, 20, 32, 29, 35, 21	⊢
	: , : , : , : , : , :
14	instantiation	30, 31, 58, 32, 33, 20, 39, 40, 35, 21	⊢
	: , : , : , : , : , :
15	theorem		⊢
	proveit.logic.equality.sub_right_side_into
16	instantiation	38, 29, 22	⊢
	: , :
17	instantiation	23, 24, 25	⊢
	: , : , :
18	instantiation	56, 49, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
20	instantiation	41	⊢
	: , :
21	instantiation	56, 46, 27	⊢
	: , : , :
22	instantiation	38, 35, 36	⊢
	: , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	30, 28, 58, 31, 34, 32, 29, 35, 36	⊢
	: , : , : , : , : , :
25	instantiation	30, 31, 58, 32, 33, 34, 39, 40, 35, 36	⊢
	: , : , : , : , : , :
26	instantiation	56, 54, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	instantiation	38, 39, 40	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.disassociation
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	41	⊢
	: , :
34	instantiation	41	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
36	instantiation	56, 46, 42	⊢
	: , : , :
37	instantiation	56, 43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
39	instantiation	56, 46, 45	⊢
	: , : , :
40	instantiation	56, 46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	56, 49, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
44	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
45	instantiation	56, 49, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	56, 51, 52	⊢
	: , : , :
48	instantiation	56, 54, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	56, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
53	assumption		⊢
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	56, 57, 58	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2