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	25	⊢
2	instantiation	18, 4	⊢
	: , : , :
3	instantiation	5, 31, 6, 45, 9, 7^*	⊢
	: , : , :
4	instantiation	8, 31, 52, 47, 9, 10^*	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
6	instantiation	11, 52, 47	⊢
	: , :
7	instantiation	25, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
9	instantiation	14, 56	⊢
	:
10	instantiation	15, 38, 16, 17^*	⊢
	: , :
11	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
12	instantiation	18, 19	⊢
	: , : , :
13	instantiation	20, 21, 22, 23^*	⊢
	: , :
14	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
15	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
16	instantiation	68, 46, 54	⊢
	: , : , :
17	instantiation	24, 38	⊢
	:
18	axiom		⊢
	proveit.logic.equality.substitution
19	instantiation	25, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
21	instantiation	68, 28, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
23	instantiation	30, 31	⊢
	:
24	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
25	axiom		⊢
	proveit.logic.equality.equals_transitivity
26	instantiation	32, 33, 63, 70, 34, 35, 38, 39, 36	⊢
	: , : , : , : , : , :
27	instantiation	37, 38, 39, 40	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29	instantiation	68, 41, 42	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
31	instantiation	68, 46, 43	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.disassociation
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
35	instantiation	44	⊢
	: , :
36	instantiation	68, 46, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
38	instantiation	68, 46, 52	⊢
	: , : , :
39	instantiation	68, 46, 47	⊢
	: , : , :
40	instantiation	48	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
42	instantiation	68, 49, 50	⊢
	: , : , :
43	instantiation	68, 61, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	instantiation	53, 52	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	53, 54	⊢
	:
48	axiom		⊢
	proveit.logic.equality.equals_reflexivity
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50	instantiation	68, 55, 56	⊢
	: , : , :
51	instantiation	68, 66, 57	⊢
	: , : , :
52	instantiation	58, 59, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.real_closure
54	instantiation	68, 61, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	instantiation	68, 69, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
59	instantiation	64, 65	⊢
	: , :
60	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
62	instantiation	68, 66, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
64	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	68, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements