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, 4, 5, 6^, 7^	, , , , ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	51	⊢
3	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
4	reference	20	⊢
5	instantiation	8, 9	⊢
	:
6	instantiation	10, 11, 12, 13	, , , , ⊢
	: , : , : , :
7	instantiation	14, 49, 47, 15, 16	, ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
10	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
11	instantiation	17, 42	⊢
	:
12	instantiation	52	⊢
	:
13	instantiation	18, 19	, , , , ⊢
	: , :
14	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
15	instantiation	63, 56, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
17	theorem		⊢
	proveit.numbers.addition.elim_zero_left
18	theorem		⊢
	proveit.logic.equality.equals_reversal
19	instantiation	21, 22, 23, 24, 25, 26, 42, 27, 49, 28^*	, , , , ⊢
	: , : , : , : , : , :
20	instantiation	63, 29, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.association
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	31	⊢
	: , :
26	instantiation	31	⊢
	: , :
27	instantiation	63, 56, 32	⊢
	: , : , :
28	instantiation	33, 34, 35	, , , , ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	63, 36, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32	instantiation	63, 61, 38	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	39, 40	, , , , ⊢
	: , : , :
35	instantiation	41, 49, 42, 43	, ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	63, 44, 45	⊢
	: , : , :
38	assumption		⊢
39	axiom		⊢
	proveit.logic.equality.substitution
40	instantiation	46, 47, 48, 49, 50	, , ⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_21
42	instantiation	63, 56, 51	⊢
	: , : , :
43	instantiation	52	⊢
	:
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
46	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
47	instantiation	63, 53, 54	⊢
	: , : , :
48	instantiation	63, 56, 55	⊢
	: , : , :
49	instantiation	63, 56, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
51	instantiation	63, 61, 58	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.equals_reflexivity
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.complex_nonzero_within_complex
54	instantiation	63, 59, 60	⊢
	: , : , :
55	instantiation	63, 61, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	assumption		⊢
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
60	instantiation	63, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
62	assumption		⊢
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real_nonzero
65	assumption		⊢
^*equality replacement requirements