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^	, , ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.division.frac_cancel_left
2	instantiation	7, 12, 8	, ⊢
	:
3	instantiation	44, 9, 10	⊢
	: , : , :
4	reference	14	, ⊢
5	instantiation	11, 12	⊢
	:
6	instantiation	13, 14	, ⊢
	:
7	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
8	instantiation	15, 16	⊢
	: , :
9	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
10	instantiation	44, 17, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
12	instantiation	19, 20, 21	⊢
	: , :
13	theorem		⊢
	proveit.numbers.division.frac_one_denom
14	instantiation	22, 30, 23	, ⊢
	: , :
15	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
16	instantiation	24, 25	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
18	instantiation	44, 26, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
20	instantiation	44, 31, 28	⊢
	: , : , :
21	instantiation	29, 30	⊢
	:
22	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
23	instantiation	44, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
27	instantiation	44, 33, 34	⊢
	: , : , :
28	instantiation	44, 36, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.negation.complex_closure
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	44, 36, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
35	instantiation	44, 38, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	44, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , :
40	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
41	instantiation	44, 45, 43	⊢
	: , : , :
42	instantiation	44, 45, 46	⊢
	: , : , :
43	assumption		⊢
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.nat1
^*equality replacement requirements