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, 5	⊢
	: , : , :
3	instantiation	6, 7	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 40, 9, 41, 42, 10, 49, 50, 44, 12	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.logic.equality.equals_reversal
7	instantiation	11, 23, 12, 13, 14, 15^, 16^	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
10	instantiation	17	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.division.prod_of_fracs
12	instantiation	64, 54, 18	⊢
	: , : , :
13	instantiation	64, 20, 19	⊢
	: , : , :
14	instantiation	64, 20, 21	⊢
	: , : , :
15	instantiation	22, 23	⊢
	:
16	instantiation	24, 25	⊢
	:
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	instantiation	64, 58, 26	⊢
	: , : , :
19	instantiation	64, 28, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21	instantiation	64, 28, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.division.frac_one_denom
23	instantiation	30, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
25	instantiation	64, 54, 33	⊢
	: , : , :
26	instantiation	64, 62, 34	⊢
	: , : , :
27	instantiation	64, 36, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
29	instantiation	64, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.logic.equality.sub_right_side_into
31	instantiation	48, 38, 44	⊢
	: , :
32	instantiation	39, 40, 66, 41, 42, 43, 49, 50, 44	⊢
	: , : , : , : , : , :
33	instantiation	64, 58, 45	⊢
	: , : , :
34	assumption		⊢
35	instantiation	64, 47, 46	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37	instantiation	64, 47, 57	⊢
	: , : , :
38	instantiation	48, 49, 50	⊢
	: , :
39	theorem		⊢
	proveit.numbers.multiplication.disassociation
40	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
42	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
43	instantiation	51	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
45	instantiation	64, 62, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
48	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
49	instantiation	64, 54, 53	⊢
	: , : , :
50	instantiation	64, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	instantiation	64, 56, 57	⊢
	: , : , :
53	instantiation	64, 58, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	64, 60, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
57	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	64, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	64, 65, 66	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements