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, 5, 6, 7, 8	⊢
	: , : , : , : , : , : , :
1	theorem		⊢
	proveit.physics.quantum.circuits.trivial_expansion_below
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
3	reference	41	⊢
4	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
5	reference	19	⊢
6	instantiation	9, 10, 11	⊢
	: , : , :
7	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
8	instantiation	12, 13, 14, 15	⊢
	: , : , : , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	16, 17, 18, 19	⊢
	: , : , : , :
11	axiom		⊢
	proveit.physics.quantum.QPE._Psi_def
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	28, 38	⊢
	: , :
14	instantiation	20	⊢
	:
15	instantiation	21, 22	⊢
	: , :
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
17	instantiation	23, 34	⊢
	:
18	instantiation	24, 34, 25	⊢
	: , : , :
19	instantiation	26, 27	⊢
	: , :
20	axiom		⊢
	proveit.logic.equality.equals_reflexivity
21	theorem		⊢
	proveit.logic.equality.equals_reversal
22	instantiation	28, 38	⊢
	: , :
23	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
24	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
25	instantiation	29, 30, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
27	instantiation	32, 41	⊢
	:
28	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
29	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
30	instantiation	33, 34	⊢
	:
31	instantiation	35, 41	⊢
	:
32	theorem		⊢
	proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
33	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
34	instantiation	36, 37, 38	⊢
	: , :
35	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
36	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	instantiation	39, 40, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
41	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos