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	, ⊢
	:
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
2	reference	32	⊢
3	instantiation	4, 5, 35, 6, 7, 8^, 9^	, ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
5	instantiation	10, 35	⊢
	:
6	instantiation	11, 32, 35	⊢
	: , :
7	instantiation	12, 35, 32, 13, 14	, ⊢
	: , : , :
8	instantiation	15, 31, 28	⊢
	: , :
9	instantiation	16, 17, 18	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.negation.real_closure
11	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
12	theorem		⊢
	proveit.numbers.ordering.less_add_right
13	assumption		⊢
14	instantiation	19, 42	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	20, 21, 42, 22, 23, 24, 27, 31, 25	⊢
	: , : , : , : , : , :
18	instantiation	26, 31, 27, 28	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
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	29	⊢
	: , :
25	instantiation	30, 31	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
27	instantiation	40, 34, 32	⊢
	: , : , :
28	instantiation	33	⊢
	:
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30	theorem		⊢
	proveit.numbers.negation.complex_closure
31	instantiation	40, 34, 35	⊢
	: , : , :
32	assumption		⊢
33	axiom		⊢
	proveit.logic.equality.equals_reflexivity
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	40, 36, 37	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	40, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements