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, 27, 19	, ⊢
	: , :
6	theorem		⊢
	proveit.logic.equality.equals_reversal
7	instantiation	9, 19, 27, 10, 11, 12^, 13^	, , ⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.commutation
9	theorem		⊢
	proveit.numbers.division.prod_of_fracs
10	instantiation	39, 14, 15	⊢
	: , : , :
11	instantiation	16, 17, 28	, ⊢
	: , :
12	instantiation	18, 19	⊢
	:
13	instantiation	20, 21	⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
15	instantiation	39, 22, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
17	instantiation	24, 27, 25	, ⊢
	:
18	theorem		⊢
	proveit.numbers.division.frac_one_denom
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
21	instantiation	26, 27, 28	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
23	instantiation	39, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
27	assumption		⊢
28	instantiation	39, 31, 32	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
30	instantiation	39, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	39, 35, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	39, 37, 38	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	39, 40, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements