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	45	⊢
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	43, 12, 14	⊢
	: , : , :
8	instantiation	43, 12, 11	⊢
	: , : , :
9	instantiation	43, 12, 13	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	instantiation	22, 14	⊢
	:
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
13	instantiation	15, 16, 27	⊢
	: , :
14	instantiation	17, 18, 19, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
16	instantiation	43, 35, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
18	instantiation	22, 23	⊢
	:
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
20	assumption		⊢
21	instantiation	43, 24, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.negation.real_closure
23	instantiation	26, 27, 28, 29	⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
25	instantiation	30, 31, 32	⊢
	: , :
26	theorem		⊢
	proveit.numbers.division.div_real_closure
27	instantiation	43, 33, 34	⊢
	: , : , :
28	instantiation	43, 35, 36	⊢
	: , : , :
29	instantiation	37, 40	⊢
	:
30	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
31	instantiation	43, 39, 38	⊢
	: , : , :
32	instantiation	43, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	43, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2