Expression of type Implies

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

# build up the expression from sub-expressions
expr = Implies(And(Equals(x, a), Equals(y, b)), Implies(Equals(fab, c), Equals(fxy, c)))

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(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')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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