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	reference	8	⊢
2	instantiation	23, 11, 4	⊢
	: , :
3	instantiation	5, 6, 7	⊢
	: , : , :
4	instantiation	8, 9, 10	⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	16, 58, 12, 17, 14, 18, 11, 24, 25, 20	⊢
	: , : , : , : , : , :
7	instantiation	16, 17, 48, 12, 18, 13, 14, 30, 21, 24, 25, 20	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	23, 15, 20	⊢
	: , :
10	instantiation	16, 17, 48, 58, 18, 19, 24, 25, 20	⊢
	: , : , : , : , : , :
11	instantiation	23, 30, 21	⊢
	: , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
13	instantiation	26	⊢
	: , :
14	instantiation	22	⊢
	: , : , :
15	instantiation	23, 24, 25	⊢
	: , :
16	theorem		⊢
	proveit.numbers.multiplication.disassociation
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	instantiation	26	⊢
	: , :
20	instantiation	56, 39, 27	⊢
	: , : , :
21	instantiation	56, 39, 28	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
23	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
25	instantiation	29, 30, 31	⊢
	: , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	instantiation	32, 33, 34, 35	⊢
	: , : , :
28	instantiation	56, 36, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
30	instantiation	56, 39, 38	⊢
	: , : , :
31	instantiation	56, 39, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	instantiation	56, 43, 41	⊢
	: , : , :
35	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38	instantiation	56, 43, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	56, 43, 44	⊢
	: , : , :
41	instantiation	56, 46, 55	⊢
	: , : , :
42	instantiation	56, 46, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	56, 46, 47	⊢
	: , : , :
45	instantiation	56, 57, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	49, 50, 51	⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
50	instantiation	56, 52, 53	⊢
	: , : , :
51	instantiation	54, 55	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
53	assumption		⊢
54	theorem		⊢
	proveit.numbers.negation.int_closure
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.nat1