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.logic.equality.sub_right_side_into
2	instantiation	12, 4, 14	⊢
	: , : , :
3	instantiation	5, 6, 44, 7, 22, 8, 9, 10	⊢
	: , : , : , : , : , : , :
4	instantiation	11, 44, 34, 22	⊢
	: , : , :
5	theorem		⊢
	proveit.physics.quantum.circuits.trivial_expansion_below
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
8	instantiation	12, 13, 14	⊢
	: , : , :
9	axiom		⊢
	proveit.physics.quantum.QPE._u_ket_register
10	instantiation	15, 16, 17, 18	⊢
	: , : , : , :
11	theorem		⊢
	proveit.physics.quantum.circuits.unitary_gate_operation
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	19, 20, 21, 22	⊢
	: , : , : , :
14	axiom		⊢
	proveit.physics.quantum.QPE._Psi_def
15	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
16	instantiation	31, 41	⊢
	: , :
17	instantiation	23	⊢
	:
18	instantiation	24, 25	⊢
	: , :
19	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
20	instantiation	26, 37	⊢
	:
21	instantiation	27, 37, 28	⊢
	: , : , :
22	instantiation	29, 30	⊢
	: , :
23	axiom		⊢
	proveit.logic.equality.equals_reflexivity
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	31, 41	⊢
	: , :
26	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
27	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
28	instantiation	32, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
30	instantiation	35, 44	⊢
	:
31	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
32	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
33	instantiation	36, 37	⊢
	:
34	instantiation	38, 44	⊢
	:
35	theorem		⊢
	proveit.physics.quantum.QPE._psi_t_ket_is_normalized_vec
36	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
37	instantiation	39, 40, 41	⊢
	: , :
38	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
39	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
44	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos