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, 28, 43, 12, 5, 14, 16, 15	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	instantiation	18	⊢
	: , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	9, 43, 11, 12, 14, 16, 15	⊢
	: , : , : , : , : , : , :
8	instantiation	10, 11, 28, 43, 12, 13, 14, 15, 16, 17^*	⊢
	: , : , : , : , : , :
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	18	⊢
	: , :
14	instantiation	41, 20, 19	⊢
	: , : , :
15	instantiation	41, 20, 35	⊢
	: , : , :
16	instantiation	41, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	instantiation	41, 37, 22	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
21	instantiation	23, 35, 30, 24	⊢
	: , :
22	instantiation	41, 39, 25	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.division.div_real_closure
24	instantiation	26, 27	⊢
	: , :
25	instantiation	41, 42, 28	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
27	instantiation	29, 34, 30, 31	⊢
	: , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
29	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
30	instantiation	32, 34, 35, 36	⊢
	: , : , :
31	instantiation	33, 34, 35, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	instantiation	41, 37, 38	⊢
	: , : , :
36	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	41, 39, 40	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	41, 42, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements