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.weak_bound_via_left_term_bound
2	reference	37	⊢
3	reference	19	⊢
4	instantiation	8, 38, 44	⊢
	: , :
5	instantiation	9, 19, 38, 44, 10, 11	, ⊢
	: , : , :
6	instantiation	12, 35, 34, 13, 14	⊢
	: , : , :
7	instantiation	15, 16, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak
10	assumption		⊢
11	instantiation	18, 55	⊢
	:
12	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
13	instantiation	53, 41, 19	⊢
	: , : , :
14	instantiation	20, 21, 22	⊢
	: , : , :
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	23, 24, 25, 52, 26, 27, 30, 34, 28	⊢
	: , : , : , : , : , :
17	instantiation	29, 34, 30, 31	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
19	instantiation	53, 47, 32	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_1
22	instantiation	33, 34, 35	⊢
	: , :
23	theorem		⊢
	proveit.numbers.addition.disassociation
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	36	⊢
	: , :
28	instantiation	53, 41, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
30	instantiation	53, 41, 38	⊢
	: , : , :
31	instantiation	39	⊢
	:
32	instantiation	53, 50, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.commutation
34	instantiation	53, 41, 44	⊢
	: , : , :
35	instantiation	53, 41, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	instantiation	43, 44	⊢
	:
38	assumption		⊢
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	instantiation	53, 54, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	53, 47, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.negation.real_closure
44	instantiation	53, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
46	instantiation	53, 50, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	53, 50, 51	⊢
	: , : , :
49	instantiation	53, 54, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	53, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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.nat5
^*equality replacement requirements