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, 45, 33, 5, 10, 28	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.disassociation
5	instantiation	19	⊢
	: , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	12, 13, 33, 15, 9, 14, 10, 28, 11^*	⊢
	: , : , : , : , : , :
8	instantiation	12, 45, 33, 13, 14, 15, 16, 28, 17^*	⊢
	: , : , : , : , : , :
9	instantiation	19	⊢
	: , :
10	instantiation	43, 31, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
12	theorem		⊢
	proveit.numbers.multiplication.association
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	instantiation	19	⊢
	: , :
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	43, 31, 20	⊢
	: , : , :
17	instantiation	21, 28, 22, 23^, 24^	⊢
	: , : , :
18	instantiation	43, 39, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	instantiation	43, 39, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
23	instantiation	27, 28	⊢
	:
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
25	instantiation	43, 41, 29	⊢
	: , : , :
26	instantiation	43, 41, 30	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
28	instantiation	43, 31, 32	⊢
	: , : , :
29	instantiation	43, 44, 33	⊢
	: , : , :
30	instantiation	43, 44, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	35, 36, 37, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
37	instantiation	43, 39, 40	⊢
	: , : , :
38	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	43, 41, 42	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements