Calc
FreshVar()
FreshVars()
Inductive()
Lemma()
NewType()
PTheorem()
Proof
QExists()
QForAll()
QImplies()
Struct()
Theorem()
axiom()
cond()
define()
prove()
search()
simp()
modus()
Defn
Judgement
LemmaError
andI()
compose()
define_fix()
defns
ext()
forget()
fresh_const()
generalize()
herb()
induct_inductive()
instan()
is_defined()
is_fresh_var()
is_proof()
obtain()
rename_vars2()
specialize()
subst()
unfold()
Modus ponens for implies and equality.
>>> a,b = smt.Bools("a b") >>> ab = axiom(smt.Implies(a, b)) >>> a = axiom(a) >>> modus(ab, a) |= b >>> ab1 = axiom(smt.Eq(a.thm, b)) >>> modus(ab1, a) |= b
ab (Proof)
a (Proof)