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	⊢
	: , : , :
1	reference	6	⊢
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 7	⊢
	: , : , :
5	instantiation	8, 9	⊢
	: , :
6	axiom		⊢
	proveit.logic.equality.substitution
7	instantiation	10, 42, 11, 43, 44, 12, 51, 52, 46, 14	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.logic.equality.equals_reversal
9	instantiation	13, 25, 14, 15, 16, 17^, 18^	⊢
	: , : , : , :
10	theorem		⊢
	proveit.numbers.multiplication.association
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
12	instantiation	19	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.division.prod_of_fracs
14	instantiation	66, 56, 20	⊢
	: , : , :
15	instantiation	66, 22, 21	⊢
	: , : , :
16	instantiation	66, 22, 23	⊢
	: , : , :
17	instantiation	24, 25	⊢
	:
18	instantiation	26, 27	⊢
	:
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	instantiation	66, 60, 28	⊢
	: , : , :
21	instantiation	66, 30, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
23	instantiation	66, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.division.frac_one_denom
25	instantiation	32, 33, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
27	instantiation	66, 56, 35	⊢
	: , : , :
28	instantiation	66, 64, 36	⊢
	: , : , :
29	instantiation	66, 38, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31	instantiation	66, 38, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.sub_right_side_into
33	instantiation	50, 40, 46	⊢
	: , :
34	instantiation	41, 42, 68, 43, 44, 45, 51, 52, 46	⊢
	: , : , : , : , : , :
35	instantiation	66, 60, 47	⊢
	: , : , :
36	assumption		⊢
37	instantiation	66, 49, 48	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39	instantiation	66, 49, 59	⊢
	: , : , :
40	instantiation	50, 51, 52	⊢
	: , :
41	theorem		⊢
	proveit.numbers.multiplication.disassociation
42	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45	instantiation	53	⊢
	: , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
47	instantiation	66, 64, 54	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
51	instantiation	66, 56, 55	⊢
	: , : , :
52	instantiation	66, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
54	instantiation	66, 58, 59	⊢
	: , : , :
55	instantiation	66, 60, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	66, 62, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
59	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	66, 64, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	66, 67, 68	⊢
	: , : , :
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