Expression of type Lambda

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

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 import Lambda, P, Q, R
from proveit.logic import Implies
from proveit.logic.booleans.quantification import general_bundled_forall_Pxy_if_Qx, general_nested_forall_Pxy_if_Qx

# build up the expression from sub-expressions
expr = Lambda([P, Q, R], Implies(general_nested_forall_Pxy_if_Qx, general_bundled_forall_Pxy_if_Qx).with_wrapping_at(1))

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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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