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