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