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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5, 51, 6, 7, 8, 9, 11, 15	⊢
	: , : , : , : , : , :
3	instantiation	10, 15, 11, 12	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	instantiation	13	⊢
	: , :
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	14, 15	⊢
	:
10	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
11	instantiation	49, 18, 16	⊢
	: , : , :
12	instantiation	17	⊢
	:
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	theorem		⊢
	proveit.numbers.negation.complex_closure
15	instantiation	49, 18, 19	⊢
	: , : , :
16	instantiation	28, 20	⊢
	:
17	axiom		⊢
	proveit.logic.equality.equals_reflexivity
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
19	instantiation	21, 22, 33	⊢
	: , :
20	instantiation	23, 24, 25, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
22	instantiation	49, 41, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
24	instantiation	28, 29	⊢
	:
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
26	assumption		⊢
27	instantiation	49, 30, 31	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.negation.real_closure
29	instantiation	32, 33, 34, 35	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
31	instantiation	36, 37, 38	⊢
	: , :
32	theorem		⊢
	proveit.numbers.division.div_real_closure
33	instantiation	49, 39, 40	⊢
	: , : , :
34	instantiation	49, 41, 42	⊢
	: , : , :
35	instantiation	43, 46	⊢
	:
36	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
37	instantiation	49, 45, 44	⊢
	: , : , :
38	instantiation	49, 45, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	49, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2