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