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, 8, 9^, 10^	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	reference	68	⊢
3	reference	56	⊢
4	instantiation	39	⊢
	: , :
5	reference	26	⊢
6	instantiation	66, 54, 11	⊢
	: , : , :
7	instantiation	66, 54, 60	⊢
	: , : , :
8	reference	51	⊢
9	instantiation	19, 12, 13	⊢
	: , : , :
10	instantiation	14, 68, 26, 51	⊢
	: , : , : , :
11	instantiation	66, 15, 16	⊢
	: , : , :
12	instantiation	17, 68, 56, 18, 26, 51	⊢
	: , : , : , : , : , :
13	instantiation	19, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
16	instantiation	22, 23, 24	⊢
	: , :
17	theorem		⊢
	proveit.numbers.multiplication.disassociation
18	instantiation	39	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	28, 29, 56, 31, 25, 30, 26, 51, 27^*	⊢
	: , : , : , : , : , :
21	instantiation	28, 68, 56, 29, 30, 31, 32, 51, 33^*	⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
23	instantiation	66, 34, 35	⊢
	: , : , :
24	instantiation	36, 55, 37	⊢
	:
25	instantiation	39	⊢
	: , :
26	instantiation	66, 54, 38	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
28	theorem		⊢
	proveit.numbers.multiplication.association
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	instantiation	39	⊢
	: , :
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	66, 54, 40	⊢
	: , : , :
33	instantiation	41, 51, 42, 43^, 44^	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
35	instantiation	66, 45, 46	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
37	instantiation	47, 59, 60, 61	⊢
	: , : , :
38	instantiation	66, 62, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	66, 62, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
43	instantiation	50, 51	⊢
	:
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
48	instantiation	66, 64, 52	⊢
	: , : , :
49	instantiation	66, 64, 53	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
51	instantiation	66, 54, 55	⊢
	: , : , :
52	instantiation	66, 67, 56	⊢
	: , : , :
53	instantiation	66, 67, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	58, 59, 60, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
60	instantiation	66, 62, 63	⊢
	: , : , :
61	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
63	instantiation	66, 64, 65	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	66, 67, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements