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