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.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
3	instantiation	5, 12, 6, 7, 8	⊢
	: , : , :
4	instantiation	9, 10, 11	⊢
	: , :
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
6	instantiation	44	⊢
	: , :
7	instantiation	13, 12	⊢
	:
8	instantiation	13, 14	⊢
	:
9	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
10	instantiation	62, 48, 15	⊢
	: , : , :
11	instantiation	24, 16, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
13	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
14	instantiation	18, 61, 59	⊢
	: , :
15	instantiation	62, 53, 19	⊢
	: , : , :
16	instantiation	41, 27, 20	⊢
	: , :
17	instantiation	21, 22, 23	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
20	instantiation	24, 25, 26	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	32, 34, 28, 33, 30, 35, 27, 42, 43, 37	⊢
	: , : , : , : , : , :
23	instantiation	32, 33, 61, 28, 35, 29, 30, 38, 39, 42, 43, 37	⊢
	: , : , : , : , : , :
24	theorem		⊢
	proveit.logic.equality.sub_right_side_into
25	instantiation	41, 31, 37	⊢
	: , :
26	instantiation	32, 33, 61, 34, 35, 36, 42, 43, 37	⊢
	: , : , : , : , : , :
27	instantiation	41, 38, 39	⊢
	: , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
29	instantiation	44	⊢
	: , :
30	instantiation	40	⊢
	: , : , :
31	instantiation	41, 42, 43	⊢
	: , :
32	theorem		⊢
	proveit.numbers.multiplication.disassociation
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	44	⊢
	: , :
37	instantiation	62, 48, 45	⊢
	: , : , :
38	instantiation	62, 48, 46	⊢
	: , : , :
39	instantiation	62, 48, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
43	instantiation	62, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	instantiation	62, 51, 50	⊢
	: , : , :
46	instantiation	62, 51, 52	⊢
	: , : , :
47	instantiation	62, 53, 54	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
50	instantiation	62, 56, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	62, 56, 58	⊢
	: , : , :
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	instantiation	57, 58, 59	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
57	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
58	instantiation	62, 60, 61	⊢
	: , : , :
59	instantiation	62, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
64	assumption		⊢