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	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
2	instantiation	4, 5	, ⊢
	: , :
3	instantiation	6, 33, 36, 7^*	⊢
	: , :
4	theorem		⊢
	proveit.numbers.ordering.relax_less
5	instantiation	8, 9	, ⊢
	: , :
6	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
7	instantiation	10, 35	⊢
	:
8	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
9	instantiation	11, 39, 18, 12, 13, 14^, 15^	, ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.negation.double_negation
11	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
12	instantiation	53, 46, 16	⊢
	: , : , :
13	instantiation	17, 18, 40, 42, 19, 20	⊢
	: , : , :
14	instantiation	21, 33	⊢
	:
15	instantiation	22, 23, 24	⊢
	: , : , :
16	assumption		⊢
17	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
19	instantiation	25, 50	⊢
	:
20	instantiation	26, 27	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.elim_zero_left
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	28, 29, 55, 30, 31, 32, 35, 36, 33	⊢
	: , : , : , : , : , :
24	instantiation	34, 35, 36, 37	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	theorem		⊢
	proveit.numbers.addition.disassociation
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	38	⊢
	: , :
33	instantiation	53, 41, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
35	instantiation	53, 41, 40	⊢
	: , : , :
36	instantiation	53, 41, 42	⊢
	: , : , :
37	instantiation	43	⊢
	:
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	instantiation	53, 44, 45	⊢
	: , : , :
40	instantiation	53, 46, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	53, 47, 48	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.equals_reflexivity
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonpos_within_real
45	instantiation	49, 50	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	53, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.negation.real_nonpos_closure
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements