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^*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.division.div_as_mult
2	instantiation	76, 54, 6	⊢
	: , : , :
3	instantiation	76, 54, 7	⊢
	: , : , :
4	instantiation	22, 11	⊢
	:
5	instantiation	33, 8, 9	⊢
	: , : , :
6	instantiation	66, 67, 10	⊢
	: , : , :
7	instantiation	66, 67, 11	⊢
	: , : , :
8	instantiation	26, 12	⊢
	: , : , :
9	instantiation	13, 39, 14, 53, 17, 15^*	⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
11	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
12	instantiation	16, 39, 60, 55, 17, 18^*	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
14	instantiation	19, 60, 55	⊢
	: , :
15	instantiation	33, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
17	instantiation	22, 64	⊢
	:
18	instantiation	23, 46, 24, 25^*	⊢
	: , :
19	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
20	instantiation	26, 27	⊢
	: , : , :
21	instantiation	28, 29, 30, 31^*	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
23	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
24	instantiation	76, 54, 62	⊢
	: , : , :
25	instantiation	32, 46	⊢
	:
26	axiom		⊢
	proveit.logic.equality.substitution
27	instantiation	33, 34, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
29	instantiation	76, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
31	instantiation	38, 39	⊢
	:
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	40, 41, 71, 78, 42, 43, 46, 47, 44	⊢
	: , : , : , : , : , :
35	instantiation	45, 46, 47, 48	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
37	instantiation	76, 49, 50	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
39	instantiation	76, 54, 51	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.addition.disassociation
41	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
42	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
43	instantiation	52	⊢
	: , :
44	instantiation	76, 54, 53	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
46	instantiation	76, 54, 60	⊢
	: , : , :
47	instantiation	76, 54, 55	⊢
	: , : , :
48	instantiation	56	⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
50	instantiation	76, 57, 58	⊢
	: , : , :
51	instantiation	76, 69, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
53	instantiation	61, 60	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	61, 62	⊢
	:
56	axiom		⊢
	proveit.logic.equality.equals_reflexivity
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
58	instantiation	76, 63, 64	⊢
	: , : , :
59	instantiation	76, 74, 65	⊢
	: , : , :
60	instantiation	66, 67, 68	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.negation.real_closure
62	instantiation	76, 69, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
65	instantiation	76, 77, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
67	instantiation	72, 73	⊢
	: , :
68	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	76, 74, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
72	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements