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, 6, 42, 8, 10, 9, 11	⊢
	: , : , : , : , : , : , :
3	instantiation	5, 42, 45, 6, 7, 8, 9, 10, 11	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	theorem		⊢
	proveit.numbers.multiplication.association
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	instantiation	12	⊢
	: , :
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	43, 21, 13	⊢
	: , : , :
10	instantiation	43, 21, 32	⊢
	: , : , :
11	instantiation	43, 21, 14	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	43, 15, 16	⊢
	: , : , :
14	instantiation	43, 17, 18	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
18	instantiation	19, 20	⊢
	:
19	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
20	instantiation	43, 21, 22	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
22	instantiation	23, 24, 27, 25	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
24	instantiation	26, 27	⊢
	:
25	instantiation	28, 29	⊢
	:
26	theorem		⊢
	proveit.numbers.negation.real_closure
27	instantiation	30, 31, 32, 33	⊢
	: , :
28	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.division.div_real_closure
31	instantiation	43, 35, 34	⊢
	: , : , :
32	instantiation	43, 35, 36	⊢
	: , : , :
33	instantiation	37, 38	⊢
	:
34	instantiation	43, 40, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	43, 40, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	instantiation	43, 44, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	43, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.nat2