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	8	⊢
2	instantiation	24, 4	⊢
	: , : , :
3	instantiation	5, 6, 7^*	⊢
	:
4	instantiation	8, 9, 10	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
6	instantiation	11, 12	⊢
	:
7	instantiation	13, 14, 18, 15^*	⊢
	: , :
8	axiom		⊢
	proveit.logic.equality.equals_transitivity
9	instantiation	24, 16	⊢
	: , : , :
10	instantiation	17, 23, 18	⊢
	: , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonpos_if_in_real_nonpos
12	instantiation	49, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
14	instantiation	49, 31, 21	⊢
	: , : , :
15	instantiation	22, 23	⊢
	:
16	instantiation	24, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
18	instantiation	49, 31, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real_nonpos
20	instantiation	27, 30, 28	⊢
	: , :
21	instantiation	49, 29, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.negation.double_negation
23	instantiation	49, 31, 32	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.substitution
25	instantiation	33, 34	⊢
	:
26	instantiation	49, 35, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.addition.add_real_neg_closure_bin
28	instantiation	49, 37, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
30	instantiation	39, 48	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	49, 40, 48	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
34	instantiation	41, 42	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	49, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
38	instantiation	49, 45, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.negation.real_neg_closure
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
41	theorem		⊢
	proveit.numbers.ordering.relax_less
42	instantiation	47, 48	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	49, 50, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
46	instantiation	52, 53	⊢
	:
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
48	assumption		⊢
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
52	theorem		⊢
	proveit.numbers.negation.int_neg_closure
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
^*equality replacement requirements