Expression of type Lambda

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, 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 = 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(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..

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	13, 21
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 21
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operands: 11
9	ExprRange	lambda_map: 12 start_index: 16 end_index: 17
10	Literal
11	ExprTuple	13
12	Lambda	parameter: 24 body: 14
13	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
14	Operation	operator: 18 operands: 19
15	Lambda	parameter: 24 body: 20
16	Literal
17	Variable
18	Literal
19	ExprTuple	20, 21
20	IndexedVar	variable: 22 index: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable