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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	31, 4	⊢
	: , : , :
3	instantiation	5, 41, 6^*	⊢
	: , :
4	modus ponens	7, 8	⊢
5	axiom		⊢
	proveit.linear_algebra.addition.vec_sum_single
6	instantiation	9, 10, 11, 12, 13, 14, 15, 16, 17	⊢
	: , : , : , :
7	instantiation	18, 19	⊢
	: , : , : , : , : , :
8	generalization	20	⊢
9	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	21	⊢
	: , : , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	42, 36, 22	⊢
	: , : , :
15	instantiation	42, 36, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
17	instantiation	42, 36, 24	⊢
	: , : , :
18	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
20	instantiation	31, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22	instantiation	42, 38, 26	⊢
	: , : , :
23	instantiation	42, 27, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
25	instantiation	31, 29	⊢
	: , : , :
26	instantiation	42, 40, 30	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
29	instantiation	31, 32	⊢
	: , : , :
30	instantiation	42, 43, 33	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.substitution
32	instantiation	34, 35	⊢
	:
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
34	theorem		⊢
	proveit.numbers.addition.elim_zero_left
35	instantiation	42, 36, 37	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	42, 38, 39	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	42, 40, 41	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements