Show the Proof

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

	step type	requirements	statement
0	instantiation	1, 2, 3	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
2	instantiation	4, 8, 5, 17, 19, 6*	⊢
	: , : , :
3	instantiation	7, 8, 9, 10, 11, 12, 13, 14	⊢
	: , : , : , :
4	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
5	instantiation	20	⊢
	: , :
6	instantiation	15, 16, 30, 32	⊢
	: , : , :
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
8	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
9	instantiation	20	⊢
	: , :
10	instantiation	18, 17	⊢
	:
11	instantiation	18, 19	⊢
	:
12	instantiation	20	⊢
	: , :
13	instantiation	21, 22	⊢
	: , :
14	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
15	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
16	instantiation	35, 23, 24	⊢
	: , : , :
17	instantiation	26, 37, 25	⊢
	: , :
18	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
19	instantiation	26, 37, 27	⊢
	: , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
22	theorem		⊢
	proveit.physics.quantum.QPE._Psi_ket_is_normalized_vec
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	35, 28, 29	⊢
	: , : , :
25	instantiation	35, 31, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
27	instantiation	35, 31, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
29	instantiation	35, 33, 34	⊢
	: , : , :
30	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
31	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
32	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
34	instantiation	35, 36, 37	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements