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