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Expression of type Equals

from the theory of proveit.numbers.ordering

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 Conditional, ConditionalSet, b, c
from proveit.logic import Equals, FALSE
from proveit.numbers import Less, LessEq
In [2]:
# build up the expression from sub-expressions
expr = Equals(ConditionalSet(Conditional(b, LessEq(b, c)), Conditional(c, Less(c, b))), ConditionalSet(b, Conditional(c, FALSE))).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left\{\begin{array}{ccc}b \textrm{ if } b \leq c \\ c \textrm{ if } c < b\end{array}\right.. =  \\ \left\{\begin{array}{ccc}b \\ c \textrm{ if } \bot\end{array}\right.. \end{array} \end{array}
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.()(2)('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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple19, 10
8Conditionalvalue: 19
condition: 11
9Conditionalvalue: 18
condition: 12
10Conditionalvalue: 18
condition: 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13Literal
14Literal
15ExprTuple19, 18
16Literal
17ExprTuple18, 19
18Variable
19Variable