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	reference	9	⊢
2	instantiation	12, 4	⊢
	: , : , :
3	instantiation	12, 5	⊢
	: , : , :
4	instantiation	6, 16	⊢
	:
5	instantiation	7, 15, 26, 31, 8^*	⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
7	theorem		⊢
	proveit.numbers.division.div_as_mult
8	instantiation	9, 10, 11	⊢
	: , : , :
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	12, 13	⊢
	: , : , :
11	instantiation	14, 15, 16	⊢
	: , :
12	axiom		⊢
	proveit.logic.equality.substitution
13	instantiation	17, 18, 19, 20^*	⊢
	: , :
14	theorem		⊢
	proveit.numbers.multiplication.commutation
15	instantiation	48, 34, 21	⊢
	: , : , :
16	instantiation	48, 34, 22	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
18	instantiation	48, 23, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
20	instantiation	25, 26	⊢
	:
21	instantiation	48, 27, 28	⊢
	: , : , :
22	instantiation	29, 30, 35, 31	⊢
	: , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
24	instantiation	48, 32, 33	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
26	instantiation	48, 34, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
29	theorem		⊢
	proveit.numbers.division.div_real_closure
30	instantiation	48, 40, 36	⊢
	: , : , :
31	instantiation	37, 44	⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33	instantiation	48, 38, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	48, 40, 41	⊢
	: , : , :
36	instantiation	48, 45, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39	instantiation	48, 43, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	48, 45, 46	⊢
	: , : , :
42	instantiation	48, 49, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	48, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
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
^*equality replacement requirements