# from the theory of proveit.logic.sets.unification¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, m, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, InSet, Union
from proveit.logic.sets import x_in_any_A
from proveit.numbers import NaturalPos

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = InSet(x, Union(A_1_to_m)), condition = x_in_any_A), InSet(m, NaturalPos))))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(m \mapsto \left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}~|~\left(x \in A_{1}\right) \lor  \left(x \in A_{2}\right) \lor  \ldots \lor  \left(x \in A_{m}\right)}~\left(x \in \left(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right)\right) \textrm{ if } m \in \mathbb{N}^+\right..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 27
body: 3
2ExprTuple27
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 28
operands: 8
6Literal
7ExprTuple9
8ExprTuple27, 10
9Lambdaparameters: 11
body: 12
10Literal
11ExprTuple30, 23
12Conditionalvalue: 13
condition: 14
13Operationoperator: 28
operands: 15
14Operationoperator: 16
operands: 17
15ExprTuple30, 18
16Literal
17ExprTuple19
18Operationoperator: 20
operands: 21
19ExprRangelambda_map: 22
start_index: 26
end_index: 27
20Literal
21ExprTuple23
22Lambdaparameter: 34
body: 24
23ExprRangelambda_map: 25
start_index: 26
end_index: 27
24Operationoperator: 28
operands: 29
25Lambdaparameter: 34
body: 31
26Literal
27Variable
28Literal
29ExprTuple30, 31
30Variable
31IndexedVarvariable: 32
index: 34
32Variable
33ExprTuple34
34Variable