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	42	⊢
2	instantiation	54, 4	⊢
	: , : , :
3	instantiation	8, 5, 6	⊢
	: , : , :
4	instantiation	54, 7	⊢
	: , : , :
5	instantiation	8, 9, 10	⊢
	: , : , :
6	instantiation	11, 12, 13, 14	⊢
	: , : , : , :
7	instantiation	42, 15, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	17, 30, 18, 19	⊢
	: , : , : , : , :
10	instantiation	42, 20, 21	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
12	instantiation	54, 22	⊢
	: , : , :
13	instantiation	54, 22	⊢
	: , : , :
14	instantiation	61, 30	⊢
	:
15	instantiation	42, 23, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
17	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
18	instantiation	75, 26, 25	⊢
	: , : , :
19	instantiation	75, 26, 27	⊢
	: , : , :
20	instantiation	54, 28	⊢
	: , : , :
21	instantiation	54, 29	⊢
	: , : , :
22	instantiation	51, 30	⊢
	:
23	instantiation	54, 31	⊢
	: , : , :
24	instantiation	54, 32	⊢
	: , : , :
25	instantiation	75, 33, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
27	instantiation	75, 35, 36	⊢
	: , : , :
28	instantiation	54, 37	⊢
	: , : , :
29	instantiation	42, 38, 39	⊢
	: , : , :
30	instantiation	75, 69, 40	⊢
	: , : , :
31	instantiation	42, 41, 44	⊢
	: , : , :
32	instantiation	42, 43, 44	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
34	instantiation	75, 45, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
36	instantiation	47, 48	⊢
	:
37	instantiation	49, 62	⊢
	:
38	instantiation	54, 50	⊢
	: , : , :
39	instantiation	51, 62	⊢
	:
40	instantiation	75, 71, 52	⊢
	: , : , :
41	instantiation	54, 53	⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	54, 55	⊢
	: , : , :
44	instantiation	56, 67	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46	instantiation	75, 57, 58	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.exponentiation.sqrt_real_pos_closure
48	instantiation	75, 59, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
50	instantiation	61, 62	⊢
	:
51	theorem		⊢
	proveit.numbers.division.frac_one_denom
52	instantiation	75, 73, 63	⊢
	: , : , :
53	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_norm
54	axiom		⊢
	proveit.logic.equality.substitution
55	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_norm
56	theorem		⊢
	proveit.numbers.exponentiation.exponentiated_one
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
60	instantiation	75, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
62	instantiation	66, 67	⊢
	:
63	instantiation	75, 76, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
66	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
67	instantiation	75, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	75, 71, 72	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	75, 73, 74	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	75, 76, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat2