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	14	⊢
2	instantiation	14, 4, 5	, , , , ⊢
	: , : , :
3	instantiation	6, 12	, , ⊢
	:
4	instantiation	7, 8	, , , ⊢
	: , : , :
5	instantiation	9, 10, 11, 12, 13^*	, , , , ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.division.frac_one_denom
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	14, 15, 16	, , , ⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.division.frac_cancel_left
10	instantiation	17, 30, 18	, ⊢
	:
11	instantiation	46, 19, 20	⊢
	: , : , :
12	instantiation	46, 39, 21	, , ⊢
	: , : , :
13	instantiation	22, 30	⊢
	:
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	23, 27, 26, 29, 28, 31, 32, 30	, , , ⊢
	: , : , : , : , : , : , :
16	instantiation	24, 25, 26, 27, 28, 29, 30, 31, 32	, , , ⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
18	assumption		⊢
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20	instantiation	46, 33, 34	⊢
	: , : , :
21	instantiation	35, 38, 40	, , ⊢
	: , :
22	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
23	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
24	theorem		⊢
	proveit.numbers.multiplication.association
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	instantiation	36	⊢
	: , :
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	46, 39, 37	⊢
	: , : , :
31	instantiation	46, 39, 38	⊢
	: , : , :
32	instantiation	46, 39, 40	, ⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
34	instantiation	46, 41, 42	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	assumption		⊢
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	43, 44, 45	, ⊢
	: , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
42	instantiation	46, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
44	assumption		⊢
45	assumption		⊢
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