# 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, 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 = 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\{\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..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 25
operands: 5
3Literal
4ExprTuple6
5ExprTuple24, 7
6Lambdaparameters: 8
body: 9
7Literal
8ExprTuple27, 20
9Conditionalvalue: 10
condition: 11
10Operationoperator: 25
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple27, 15
13Literal
14ExprTuple16
15Operationoperator: 17
operands: 18
16ExprRangelambda_map: 19
start_index: 23
end_index: 24
17Literal
18ExprTuple20
19Lambdaparameter: 31
body: 21
20ExprRangelambda_map: 22
start_index: 23
end_index: 24
21Operationoperator: 25
operands: 26
22Lambdaparameter: 31
body: 28
23Literal
24Variable
25Literal
26ExprTuple27, 28
27Variable
28IndexedVarvariable: 29
index: 31
29Variable
30ExprTuple31
31Variable