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