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	theorem		⊢
	proveit.numbers.absolute_value.abs_even
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8, 9, 18, 19, 20, 10^, 11^	⊢
	: , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	44, 27, 12	⊢
	: , : , :
6	instantiation	13, 14, 46, 15, 16, 17, 18, 19, 20	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
8	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
9	instantiation	21	⊢
	: , : , :
10	instantiation	23, 22	⊢
	:
11	instantiation	23, 24	⊢
	:
12	instantiation	32, 25, 28	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.disassociation
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	instantiation	26	⊢
	: , :
18	instantiation	44, 27, 33	⊢
	: , : , :
19	instantiation	44, 27, 34	⊢
	: , : , :
20	instantiation	44, 27, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
22	instantiation	29, 46	⊢
	:
23	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
24	instantiation	30, 31	⊢
	: , :
25	instantiation	32, 33, 34	⊢
	: , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	35, 36	⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
30	theorem		⊢
	proveit.numbers.ordering.relax_less
31	instantiation	37, 41	⊢
	:
32	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
33	instantiation	44, 38, 39	⊢
	: , : , :
34	instantiation	44, 40, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
36	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	44, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	44, 45, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements