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^*	, , , , ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	5, 6	, ⊢
	: , : , :
3	instantiation	7, 8	, , , , ⊢
	: , :
4	instantiation	9, 24, 25, 10, 11^*	, , , ⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	12, 38, 27	, ⊢
	: , :
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	13, 27, 38, 14, 15, 16^, 17^	, , , , ⊢
	: , : , : , :
9	theorem		⊢
	proveit.numbers.division.frac_cancel_left
10	instantiation	46, 18, 19	⊢
	: , : , :
11	instantiation	20, 38	⊢
	:
12	theorem		⊢
	proveit.numbers.multiplication.commutation
13	theorem		⊢
	proveit.numbers.division.prod_of_fracs
14	instantiation	46, 21, 22	⊢
	: , : , :
15	instantiation	23, 24, 25	, , , ⊢
	: , :
16	instantiation	26, 27	⊢
	:
17	instantiation	28, 29	, ⊢
	:
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
19	instantiation	46, 30, 31	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22	instantiation	46, 32, 33	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_complex_nonzero_closure_bin
24	instantiation	35, 38, 34	, ⊢
	:
25	instantiation	35, 39, 36	, ⊢
	:
26	theorem		⊢
	proveit.numbers.division.frac_one_denom
27	assumption		⊢
28	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
29	instantiation	37, 38, 39	, ⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
31	instantiation	46, 40, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33	instantiation	46, 42, 43	⊢
	: , : , :
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
38	assumption		⊢
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	46, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43	instantiation	46, 47, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
46	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
^*equality replacement requirements