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	10	⊢
2	instantiation	10, 3	⊢
	: , : , :
3	instantiation	4, 5, 6	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	10, 7	⊢
	: , : , :
6	instantiation	8, 13, 14, 15, 16, 20, 17, 18, 9^*	⊢
	: , : , : , : , :
7	instantiation	10, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
9	instantiation	12, 13, 14, 15, 16, 17, 18	⊢
	: , : , : , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	19, 20, 27, 21^*	⊢
	: , :
12	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	22	⊢
	: , :
17	instantiation	62, 32, 23	⊢
	: , : , :
18	instantiation	62, 32, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
20	instantiation	62, 32, 25	⊢
	: , : , :
21	instantiation	26, 27	⊢
	:
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	instantiation	62, 30, 28	⊢
	: , : , :
24	instantiation	62, 30, 29	⊢
	: , : , :
25	instantiation	62, 30, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
27	instantiation	62, 32, 33	⊢
	: , : , :
28	instantiation	62, 37, 34	⊢
	: , : , :
29	instantiation	62, 35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
31	instantiation	62, 37, 54	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	38, 39, 57	⊢
	: , : , :
34	instantiation	62, 40, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
36	instantiation	42, 43, 44	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
39	instantiation	45, 46	⊢
	: , :
40	instantiation	47, 48, 59	⊢
	: , :
41	assumption		⊢
42	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
43	instantiation	62, 49, 50	⊢
	: , : , :
44	instantiation	58, 51	⊢
	:
45	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
48	instantiation	52, 53, 54	⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50	instantiation	62, 55, 56	⊢
	: , : , :
51	instantiation	62, 63, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
53	instantiation	58, 59	⊢
	:
54	instantiation	62, 60, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
58	theorem		⊢
	proveit.numbers.negation.int_closure
59	instantiation	62, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
64	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements