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T proof of L : P
has a companion
proof of L : P
which we shall refer to as the plain proof constructor.
The plain proof constructor tactic evaluates
in order to prove
. Tactic evaluation is similar to macro expansion and rendering.
The T proof constructor uses the tactic definition of
to prove
. Thus, the T proof constructor allows to customize tactic evaluation on a per theory basis whereas the the plain proof constructor treats all proofs equally.
As an example of a proof which uses the plain construct, consider the following proof of Lemma 1.8 in Mendelson: 'Introduction to mathematical logic'.


In Line
we assume propositional calculus
as defined on the Peano page.
In Line
we use Axiom
of
to prove
. Line
and
are similar.
In Line
we apply Modus Ponens
of
to Line
and
to conclude
. Line
is similar.
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