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^*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.division.div_as_mult
2	reference	13	⊢
3	reference	23	⊢
4	instantiation	6, 43	⊢
	:
5	instantiation	7, 8, 9	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	10, 11	⊢
	: , : , :
9	instantiation	12, 13, 14	⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	15, 16, 41, 17^*	⊢
	: , :
12	theorem		⊢
	proveit.numbers.multiplication.commutation
13	instantiation	44, 27, 18	⊢
	: , : , :
14	instantiation	44, 27, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
16	instantiation	44, 20, 21	⊢
	: , : , :
17	instantiation	22, 23	⊢
	:
18	assumption		⊢
19	instantiation	44, 33, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21	instantiation	44, 25, 26	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
23	instantiation	44, 27, 28	⊢
	: , : , :
24	instantiation	44, 29, 30	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
26	instantiation	44, 31, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	44, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
30	instantiation	35, 36, 37	⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
32	instantiation	44, 38, 43	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	44, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
36	instantiation	44, 42, 41	⊢
	: , : , :
37	instantiation	44, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	44, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements