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.add_complex_closure_bin
2	instantiation	61, 46, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	:
4	instantiation	61, 51, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.negation.complex_closure
6	instantiation	8, 9, 10	⊢
	: , :
7	instantiation	61, 59, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
9	instantiation	61, 46, 12	⊢
	: , : , :
10	instantiation	20, 13, 14	⊢
	: , : , :
11	instantiation	61, 62, 32	⊢
	: , : , :
12	instantiation	61, 53, 15	⊢
	: , : , :
13	instantiation	38, 23, 16	⊢
	: , :
14	instantiation	17, 18, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
16	instantiation	20, 21, 22	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	30, 32, 24, 31, 26, 33, 23, 39, 40, 35	⊢
	: , : , : , : , : , :
19	instantiation	30, 31, 63, 24, 33, 25, 26, 27, 28, 39, 40, 35	⊢
	: , : , : , : , : , :
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	instantiation	38, 29, 35	⊢
	: , :
22	instantiation	30, 31, 63, 32, 33, 34, 39, 40, 35	⊢
	: , : , : , : , : , :
23	instantiation	61, 46, 36	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
25	instantiation	41	⊢
	: , :
26	instantiation	37	⊢
	: , : , :
27	instantiation	61, 46, 44	⊢
	: , : , :
28	instantiation	61, 46, 45	⊢
	: , : , :
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.numbers.numerals.decimals.nat1
33	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34	instantiation	41	⊢
	: , :
35	instantiation	61, 46, 42	⊢
	: , : , :
36	instantiation	43, 44, 45	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
38	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
40	instantiation	61, 46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	48, 49, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
44	instantiation	61, 51, 52	⊢
	: , : , :
45	instantiation	61, 53, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	55, 56	⊢
	:
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	57, 58	⊢
	: , :
50	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	61, 59, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
55	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
56	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
57	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	61, 62, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2