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^	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.right_add_eq_rational
2	reference	36	⊢
3	reference	8	⊢
4	instantiation	14, 8, 9	⊢
	: , : , :
5	reference	9	⊢
6	instantiation	10, 30	⊢
	:
7	instantiation	11, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.zero_is_rational
9	instantiation	14, 15, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.elim_zero_left
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	17, 18, 19, 20, 21, 22, 25, 23, 30	⊢
	: , : , : , : , : , :
13	instantiation	24, 30, 25, 26	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	27, 41	⊢
	:
16	assumption		⊢
17	theorem		⊢
	proveit.numbers.addition.disassociation
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	28	⊢
	: , :
23	instantiation	29, 30	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
25	instantiation	45, 33, 31	⊢
	: , : , :
26	instantiation	32	⊢
	:
27	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	theorem		⊢
	proveit.numbers.negation.complex_closure
30	instantiation	45, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
32	axiom		⊢
	proveit.logic.equality.equals_reflexivity
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	45, 35, 36	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	37, 38, 39, 40	⊢
	: , :
37	theorem		⊢
	proveit.numbers.division.div_rational_closure
38	instantiation	45, 42, 41	⊢
	: , : , :
39	instantiation	45, 42, 43	⊢
	: , : , :
40	instantiation	44, 47	⊢
	:
41	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
47	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
^*equality replacement requirements