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	14	⊢
2	instantiation	14, 4, 5	⊢
	: , : , :
3	instantiation	6, 12	⊢
	:
4	instantiation	7, 8	⊢
	: , : , :
5	instantiation	9, 10, 11, 12, 13^*	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.division.frac_one_denom
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	14, 15, 16	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.division.frac_cancel_left
10	instantiation	69, 18, 17	⊢
	: , : , :
11	instantiation	69, 18, 19	⊢
	: , : , :
12	instantiation	69, 47, 20	⊢
	: , : , :
13	instantiation	21, 27	⊢
	:
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	22, 24, 68, 26, 28, 27, 29	⊢
	: , : , : , : , : , : , :
16	instantiation	23, 68, 71, 24, 25, 26, 27, 28, 29	⊢
	: , : , : , : , : , :
17	instantiation	69, 30, 40	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19	instantiation	69, 31, 32	⊢
	: , : , :
20	instantiation	33, 58, 36	⊢
	: , :
21	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
22	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
23	theorem		⊢
	proveit.numbers.multiplication.association
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	instantiation	34	⊢
	: , :
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	69, 47, 35	⊢
	: , : , :
28	instantiation	69, 47, 58	⊢
	: , : , :
29	instantiation	69, 47, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
32	instantiation	69, 37, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	instantiation	69, 39, 40	⊢
	: , : , :
36	instantiation	69, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	69, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
42	instantiation	45, 46	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
46	instantiation	69, 47, 48	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	49, 50, 53, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
50	instantiation	52, 53	⊢
	:
51	instantiation	54, 55	⊢
	:
52	theorem		⊢
	proveit.numbers.negation.real_closure
53	instantiation	56, 57, 58, 59	⊢
	: , :
54	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
55	assumption		⊢
56	theorem		⊢
	proveit.numbers.division.div_real_closure
57	instantiation	69, 61, 60	⊢
	: , : , :
58	instantiation	69, 61, 62	⊢
	: , : , :
59	instantiation	63, 64	⊢
	:
60	instantiation	69, 66, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	69, 66, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
65	instantiation	69, 70, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	69, 70, 71	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements