Expression of type Forall

from the theory of proveit.logic.equality

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, f, fab, fxy, x, y
from proveit.logic import And, Equals, Forall, Implies

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, x, y, a, b], instance_expr = Implies(And(Equals(x, a), Equals(y, b)), Equals(fxy, fab)))

expr:

# 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

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

\forall_{f, x, y, a, b}~\left(\left(\left(x = a\right) \land \left(y = b\right)\right) \Rightarrow \left(f\left(x, y\right) = f\left(a, b\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	21, 23, 24, 25, 26
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 18 operands: 12
10	Literal
11	ExprTuple	13, 14
12	ExprTuple	15, 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 21 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	23, 25
18	Literal
19	ExprTuple	24, 26
20	ExprTuple	23, 24
21	Variable
22	ExprTuple	25, 26
23	Variable
24	Variable
25	Variable
26	Variable