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^, 7^*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
2	reference	42	⊢
3	instantiation	8, 42	⊢
	:
4	reference	37	⊢
5	instantiation	9, 33, 10	⊢
	:
6	instantiation	11, 33, 28, 12	⊢
	: , :
7	instantiation	13, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.negation.int_closure
9	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
10	instantiation	17, 16	⊢
	:
11	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
12	instantiation	17, 18	⊢
	:
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	19, 40, 20, 21, 22, 23	⊢
	: , : , : , :
15	instantiation	24, 33, 28, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
19	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
20	instantiation	26	⊢
	: , :
21	instantiation	26	⊢
	: , :
22	instantiation	27, 28	⊢
	:
23	instantiation	29, 33, 30^*	⊢
	: , :
24	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
28	instantiation	43, 35, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.negation.pos_times_neg
30	instantiation	32, 33	⊢
	:
31	instantiation	43, 38, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
33	instantiation	43, 35, 36	⊢
	: , : , :
34	instantiation	43, 41, 37	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	instantiation	43, 38, 39	⊢
	: , : , :
37	instantiation	43, 44, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	43, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements