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