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	⊢
	: , : , :
3	instantiation	6, 7	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9	⊢
	:
6	theorem		⊢
	proveit.numbers.addition.elim_zero_left
7	instantiation	39, 11, 10	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
9	instantiation	39, 11, 12	⊢
	: , : , :
10	instantiation	13, 14, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
12	instantiation	16, 17, 18, 19	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
14	instantiation	39, 24, 20	⊢
	: , : , :
15	instantiation	39, 21, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.division.div_real_closure
17	instantiation	39, 24, 23	⊢
	: , : , :
18	instantiation	39, 24, 25	⊢
	: , : , :
19	instantiation	26, 41	⊢
	:
20	instantiation	39, 27, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
23	instantiation	39, 30, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
25	instantiation	39, 30, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
27	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
28	instantiation	32, 33, 34	⊢
	: , :
29	instantiation	39, 36, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	instantiation	39, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
33	instantiation	39, 40, 38	⊢
	: , : , :
34	instantiation	39, 40, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2