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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalOC
2	reference	33	⊢
3	reference	15	⊢
4	instantiation	5, 6, 7	⊢
	: , :
5	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
6	instantiation	8, 33, 9, 10, 11, 12^, 13^	⊢
	: , : , :
7	instantiation	14, 15, 16	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
10	instantiation	39, 35, 17	⊢
	: , : , :
11	instantiation	18, 19	⊢
	:
12	instantiation	20, 21, 22	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
14	theorem		⊢
	proveit.numbers.ordering.relax_equal_to_less_eq
15	instantiation	39, 35, 23	⊢
	: , : , :
16	instantiation	24	⊢
	:
17	instantiation	39, 37, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	instantiation	26, 28	⊢
	:
22	instantiation	27, 28, 29	⊢
	: , :
23	instantiation	39, 37, 30	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	instantiation	39, 40, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.elim_zero_right
27	theorem		⊢
	proveit.numbers.addition.commutation
28	instantiation	39, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
30	instantiation	39, 40, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	39, 35, 36	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	39, 37, 38	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	39, 40, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements