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Expression of type Equals

from the theory of proveit.logic.sets.intersection

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 A, B, C, D, x
from proveit.logic import Equals, Intersect, NotInSet, Or
In [2]:
# build up the expression from sub-expressions
expr = Equals(NotInSet(x, Intersect(A, B, C, D)), Or(NotInSet(x, A), NotInSet(x, B), NotInSet(x, C), NotInSet(x, D)))
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(x \notin \left(A \cap B \cap C \cap D\right)\right) = \left(\left(x \notin A\right) \lor \left(x \notin B\right) \lor \left(x \notin C\right) \lor \left(x \notin D\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: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple23, 8
6Literal
7ExprTuple9, 10, 11, 12
8Operationoperator: 13
operands: 14
9Operationoperator: 18
operands: 15
10Operationoperator: 18
operands: 16
11Operationoperator: 18
operands: 17
12Operationoperator: 18
operands: 19
13Literal
14ExprTuple20, 21, 22, 24
15ExprTuple23, 20
16ExprTuple23, 21
17ExprTuple23, 22
18Literal
19ExprTuple23, 24
20Variable
21Variable
22Variable
23Variable
24Variable