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Expression of type Equals

from the theory of proveit.logic.sets.subtraction

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 c
from proveit.logic import Difference, Equals, InSet, NotInSet, Or, Set
from proveit.numbers import Add, four, one, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Add(one, one)
sub_expr2 = Set(one, sub_expr1, three, Add(two, two))
sub_expr3 = Set(sub_expr1, Add(two, one), four)
expr = Equals(NotInSet(c, Difference(sub_expr2, sub_expr3)), Or(NotInSet(c, sub_expr2), InSet(c, sub_expr3)))
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(c \notin \left(\left\{1, 1 + 1, 3, 2 + 2\right\} - \left\{1 + 1, 2 + 1, 4\right\}\right)\right) = \left(\left(c \notin \left\{1, 1 + 1, 3, 2 + 2\right\}\right) \lor \left(c \in \left\{1 + 1, 2 + 1, 4\right\}\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: 13
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple18, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple17, 19
13Literal
14ExprTuple18, 17
15Literal
16ExprTuple18, 19
17Operationoperator: 21
operands: 20
18Variable
19Operationoperator: 21
operands: 22
20ExprTuple33, 25, 23, 24
21Literal
22ExprTuple25, 26, 27
23Literal
24Operationoperator: 30
operands: 28
25Operationoperator: 30
operands: 29
26Operationoperator: 30
operands: 31
27Literal
28ExprTuple32, 32
29ExprTuple33, 33
30Literal
31ExprTuple32, 33
32Literal
33Literal