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	8	⊢
2	instantiation	3, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
4	instantiation	10, 7	⊢
	: , : , :
5	instantiation	8, 9	⊢
	: , :
6	instantiation	10, 11	⊢
	: , : , :
7	instantiation	12, 13, 14	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.equals_reversal
9	instantiation	15, 16, 21, 20, 17	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	18, 19, 52	⊢
	: , :
12	theorem		⊢
	proveit.numbers.addition.commutation
13	instantiation	48, 22, 20	⊢
	: , : , :
14	instantiation	48, 22, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
16	instantiation	48, 22, 23	⊢
	: , : , :
17	instantiation	24, 50	⊢
	:
18	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
19	instantiation	48, 25, 26	⊢
	: , : , :
20	instantiation	27, 28, 29	⊢
	: , : , :
21	instantiation	48, 30, 31	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
23	instantiation	48, 32, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
26	instantiation	48, 34, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
28	instantiation	36, 37	⊢
	: , :
29	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
31	instantiation	48, 38, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	48, 40, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
35	instantiation	48, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
39	instantiation	48, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	48, 46, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43	instantiation	48, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
45	instantiation	51, 52	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
51	theorem		⊢
	proveit.numbers.negation.int_neg_closure
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1