Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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, Px, Q, Qx, x
from proveit.core_expr_types import Qk_implies_Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, Set

# build up the expression from sub-expressions
expr = Lambda([a_1_to_n], Forall(instance_param_or_params = [P, Q], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n), condition = Qx), condition = Qk_implies_Pk_a1_to_an))

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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left[\forall_{P, Q~|~\left(Q\left(a_{1}\right) \Rightarrow P\left(a_{1}\right)\right), \left(Q\left(a_{2}\right) \Rightarrow P\left(a_{2}\right)\right), \ldots, \left(Q\left(a_{n}\right) \Rightarrow P\left(a_{n}\right)\right)}~\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}~|~Q\left(x\right)}~P\left(x\right)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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