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	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
2	instantiation	39, 40, 5	⊢
	: , : , :
3	reference	38	⊢
4	instantiation	15, 6, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
6	instantiation	21, 41, 8, 9, 10, 11	⊢
	: , : , : , :
7	instantiation	12, 13, 14	⊢
	:
8	instantiation	27	⊢
	: , :
9	instantiation	27	⊢
	: , :
10	instantiation	15, 16, 17	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
12	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
13	instantiation	39, 32, 18	⊢
	: , : , :
14	instantiation	19, 20	⊢
	:
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	21, 41, 22, 23, 24, 25	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
18	instantiation	39, 35, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
21	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
22	instantiation	27	⊢
	: , :
23	instantiation	27	⊢
	: , :
24	instantiation	28, 30	⊢
	:
25	instantiation	29, 30	⊢
	:
26	instantiation	39, 37, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
29	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
30	instantiation	39, 32, 33	⊢
	: , : , :
31	instantiation	39, 40, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	39, 35, 36	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
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