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