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