Theorem binary_evaluation of type Forall

from the theory of proveit.logic.equality

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.logic.equality import binary_evaluation

# check that the built expression is the same as the stored expression
assert binary_evaluation.expr == stored_expr
assert binary_evaluation.expr._style_id == stored_expr._style_id
print("Passed sanity check: binary_evaluation matches stored_expr")

Passed sanity check: binary_evaluation matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{f, x, y, a, b, c}~\left(\left(\left(x = a\right) \land \left(y = b\right)\right) \Rightarrow \left(\left(f\left(a, b\right) = c\right) \Rightarrow \left(f\left(x, y\right) = c\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	26, 30, 31, 28, 29, 24
5	Operation	operator: 11 operands: 6
6	ExprTuple	7, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 20 operands: 17
14	Operation	operator: 20 operands: 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	30, 28
18	ExprTuple	31, 29
19	ExprTuple	22, 24
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 26 operands: 25
23	Operation	operator: 26 operands: 27
24	Variable
25	ExprTuple	28, 29
26	Variable
27	ExprTuple	30, 31
28	Variable
29	Variable
30	Variable
31	Variable