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Proofgold Proof
pf
Apply nat_ind with
λ x0 .
mul_nat
0
x0
=
0
leaving 2 subgoals.
The subproof is completed by applying mul_nat_0R with
0
.
Let x0 of type
ι
be given.
Assume H0:
nat_p
x0
.
Assume H1:
mul_nat
0
x0
=
0
.
Apply mul_nat_SR with
0
,
x0
,
λ x1 x2 .
x2
=
0
leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1 with
λ x1 x2 .
add_nat
0
x2
=
0
.
The subproof is completed by applying add_nat_0R with
0
.
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