Expression of type ExprTuple

from the theory of proveit.logic.sets.unification

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, S
from proveit.core_expr_types import A_1_to_m
from proveit.logic import SubsetEq, Union
from proveit.logic.sets import each_A_in_S

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([A_1_to_m, S], Conditional(SubsetEq(Union(A_1_to_m), S), each_A_in_S)))

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(A_{1}, A_{2}, \ldots, A_{m}, S\right) \mapsto \left\{\left(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right) \subseteq S \textrm{ if } \left(A_{1} \subseteq S\right) \land  \left(A_{2} \subseteq S\right) \land  \ldots \land  \left(A_{m} \subseteq S\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	14, 22
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 22
7	Literal
8	ExprTuple	10
9	Operation	operator: 11 operands: 12
10	ExprRange	lambda_map: 13 start_index: 17 end_index: 18
11	Literal
12	ExprTuple	14
13	Lambda	parameter: 25 body: 15
14	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
15	Operation	operator: 19 operands: 20
16	Lambda	parameter: 25 body: 21
17	Literal
18	Variable
19	Literal
20	ExprTuple	21, 22
21	IndexedVar	variable: 23 index: 25
22	Variable
23	Variable
24	ExprTuple	25
25	Variable