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