Expression of type ExprTuple

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 Conditional, ExprTuple, 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 And, Forall, Set

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([P, Q], Conditional(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n), condition = Qx), And(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(\left(P, Q\right) \mapsto \left\{\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}~|~Q\left(x\right)}~P\left(x\right) \textrm{ if } \left(Q\left(a_{1}\right) \Rightarrow P\left(a_{1}\right)\right) \land  \left(Q\left(a_{2}\right) \Rightarrow P\left(a_{2}\right)\right) \land  \ldots \land  \left(Q\left(a_{n}\right) \Rightarrow P\left(a_{n}\right)\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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