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