Let R, α, β, p and q be given.
Assume Ha Hb.
Apply H1 to the current goal.
Let γ be given.
Assume H3.
Apply H3 to the current goal.
Assume H3.
Apply H3 to the current goal.
Let r be given.
Assume H3.
Apply H3 to the current goal.
Assume H3: R γ r.
We use γ to witness the existential quantifier.
Apply andI to the current goal.
An exact proof term for the current goal is Hc.
We use r to witness the existential quantifier.
Apply andI to the current goal.
An exact proof term for the current goal is H3.
An
exact proof term for the current goal is
PNoLe_tra γ α β Hc Ha Hb r p q H4 H2.
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