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, 50, 6, 7, 8, 11, 9, 12	⊢
	: , : , : , : , : , :
3	instantiation	10, 11, 12, 13	⊢
	: , : , :
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	14	⊢
	: , :
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	48, 16, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
11	instantiation	48, 16, 19	⊢
	: , : , :
12	instantiation	48, 16, 17	⊢
	: , : , :
13	instantiation	18	⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	27, 19	⊢
	:
16	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
17	instantiation	20, 21, 32	⊢
	: , :
18	axiom		⊢
	proveit.logic.equality.equals_reflexivity
19	instantiation	22, 23, 24, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
21	instantiation	48, 40, 26	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
23	instantiation	27, 28	⊢
	:
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
25	assumption		⊢
26	instantiation	48, 29, 30	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.negation.real_closure
28	instantiation	31, 32, 33, 34	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
30	instantiation	35, 36, 37	⊢
	: , :
31	theorem		⊢
	proveit.numbers.division.div_real_closure
32	instantiation	48, 38, 39	⊢
	: , : , :
33	instantiation	48, 40, 41	⊢
	: , : , :
34	instantiation	42, 45	⊢
	:
35	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
36	instantiation	48, 44, 43	⊢
	: , : , :
37	instantiation	48, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	48, 46, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	48, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2