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	27	⊢
3	reference	9	⊢
4	reference	38	⊢
5	instantiation	8, 9, 10, 40, 11, 12	⊢
	: , : , :
6	instantiation	23, 13, 14	⊢
	: , : , :
7	instantiation	15, 33, 32, 16, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.ordering.less_add_right
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
10	instantiation	51, 43, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
12	instantiation	19, 55	⊢
	:
13	instantiation	20, 21	⊢
	:
14	instantiation	31, 21, 22	⊢
	: , :
15	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
16	instantiation	51, 39, 35	⊢
	: , : , :
17	instantiation	23, 24, 25	⊢
	: , : , :
18	instantiation	51, 47, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
20	theorem		⊢
	proveit.numbers.addition.elim_zero_right
21	instantiation	51, 39, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
23	theorem		⊢
	proveit.logic.equality.sub_right_side_into
24	instantiation	28, 29, 30	⊢
	: , : , :
25	instantiation	31, 32, 33	⊢
	: , :
26	instantiation	51, 52, 54	⊢
	: , : , :
27	instantiation	34, 35	⊢
	:
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_2
31	theorem		⊢
	proveit.numbers.addition.commutation
32	instantiation	51, 39, 38	⊢
	: , : , :
33	instantiation	51, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.negation.real_closure
35	instantiation	51, 43, 41	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.substitution
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
38	instantiation	51, 43, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	51, 43, 44	⊢
	: , : , :
41	instantiation	51, 47, 45	⊢
	: , : , :
42	instantiation	51, 47, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	51, 47, 48	⊢
	: , : , :
45	instantiation	51, 52, 49	⊢
	: , : , :
46	instantiation	51, 52, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	51, 52, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
50	instantiation	53, 54, 55	⊢
	: , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements