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^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.addition.association
2	reference	56	⊢
3	reference	51	⊢
4	instantiation	30	⊢
	: , :
5	instantiation	54, 32, 9	⊢
	: , : , :
6	instantiation	54, 32, 10	⊢
	: , : , :
7	instantiation	54, 32, 46	⊢
	: , : , :
8	instantiation	11, 12, 13^*	⊢
	: , :
9	instantiation	14, 15, 16	⊢
	: , :
10	instantiation	54, 17, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	19, 20, 51, 56, 21, 22, 23, 24	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
14	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
15	instantiation	54, 49, 25	⊢
	: , : , :
16	instantiation	26, 37, 51	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
18	instantiation	27, 28, 29	⊢
	: , :
19	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	30	⊢
	: , :
23	instantiation	54, 32, 31	⊢
	: , : , :
24	instantiation	54, 32, 37	⊢
	: , : , :
25	instantiation	54, 52, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
27	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
28	instantiation	54, 34, 35	⊢
	: , : , :
29	instantiation	36, 37, 38	⊢
	:
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	instantiation	54, 49, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	54, 55, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
35	instantiation	54, 41, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
37	instantiation	43, 45, 46, 47	⊢
	: , : , :
38	instantiation	44, 45, 46, 47	⊢
	: , : , :
39	instantiation	54, 52, 48	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
46	instantiation	54, 49, 50	⊢
	: , : , :
47	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
48	instantiation	54, 55, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	54, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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