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Expression of type InSet

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import x
from proveit.logic import InSet
from proveit.logic.sets import general_unionall_Ryn
In [2]:
# build up the expression from sub-expressions
expr = InSet(x, general_unionall_Ryn)
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())
x \in \left[\bigcup_{\left(y_{1} \in S_{1}\right), \left(y_{2} \in S_{2}\right), \ldots, \left(y_{n} \in S_{n}\right)~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~R\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 20
operands: 1
1ExprTuple2, 3
2Variable
3Operationoperator: 4
operand: 6
4Literal
5ExprTuple6
6Lambdaparameters: 17
body: 7
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operands: 17
9Operationoperator: 11
operands: 12
10Variable
11Literal
12ExprTuple13, 14
13ExprRangelambda_map: 15
start_index: 23
end_index: 24
14Operationoperator: 16
operands: 17
15Lambdaparameter: 30
body: 18
16Variable
17ExprTuple19
18Operationoperator: 20
operands: 21
19ExprRangelambda_map: 22
start_index: 23
end_index: 24
20Literal
21ExprTuple26, 25
22Lambdaparameter: 30
body: 26
23Literal
24Variable
25IndexedVarvariable: 27
index: 30
26IndexedVarvariable: 28
index: 30
27Variable
28Variable
29ExprTuple30
30Variable