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Expression of type Implies

from the theory of proveit.logic.booleans

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 And, Implies, Not, TRUE
In [2]:
# build up the expression from sub-expressions
expr = Implies(And(Implies(TRUE, C), Implies(Not(TRUE), C)), C)
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(\left(\top \Rightarrow C\right) \land \left((\lnot \top) \Rightarrow C\right)\right) \Rightarrow C
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: 8
operands: 1
1ExprTuple2, 11
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple14, 11
8Literal
9ExprTuple10, 11
10Operationoperator: 12
operand: 14
11Variable
12Literal
13ExprTuple14
14Literal