Expression of type Implies

from the theory of proveit.logic.booleans.quantification.existence

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit.logic import Implies
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy, general_exists_Rz_st_Qz, general_forall_st_Qx__Px_implies_Rx

# build up the expression from sub-expressions
expr = Implies(general_forall_st_Qx__Px_implies_Rx, Implies(general_exists_Py_st_Qy, general_exists_Rz_st_Qz).with_wrapping_at(2)).with_wrapping_at(2)

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\begin{array}{c} \begin{array}{l} \left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \Rightarrow  \\ \left[\exists_{z_{1}, z_{2}, \ldots, z_{n}~|~Q\left(z_{1}, z_{2}, \ldots, z_{n}\right)}~R\left(z_{1}, z_{2}, \ldots, z_{n}\right)\right] \end{array} \end{array}\right) \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 18 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 18 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 28 body: 10
8	Operation	operator: 12 operand: 16
9	Operation	operator: 12 operand: 17
10	Conditional	value: 14 condition: 15
11	ExprTuple	16
12	Literal
13	ExprTuple	17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 32 operands: 28
16	Lambda	parameters: 30 body: 20
17	Lambda	parameters: 33 body: 21
18	Literal
19	ExprTuple	22, 23
20	Conditional	value: 24 condition: 25
21	Conditional	value: 26 condition: 27
22	Operation	operator: 29 operands: 28
23	Operation	operator: 31 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 32 operands: 30
26	Operation	operator: 31 operands: 33
27	Operation	operator: 32 operands: 33
28	ExprTuple	34
29	Variable
30	ExprTuple	35
31	Variable
32	Variable
33	ExprTuple	36
34	ExprRange	lambda_map: 37 start_index: 40 end_index: 41
35	ExprRange	lambda_map: 38 start_index: 40 end_index: 41
36	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
37	Lambda	parameter: 49 body: 42
38	Lambda	parameter: 49 body: 43
39	Lambda	parameter: 49 body: 44
40	Literal
41	Variable
42	IndexedVar	variable: 45 index: 49
43	IndexedVar	variable: 46 index: 49
44	IndexedVar	variable: 47 index: 49
45	Variable
46	Variable
47	Variable
48	ExprTuple	49
49	Variable