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Proof step 2 from proof tr-fold (previous step)

((r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P))(H) ⊦ ((tr(r, branch(t0, a, t1)) * P))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ tr(r, branch(t0, a, t1)) = _∃(λ r0, r1. r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1))
Proof step 4:
((r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P))(H) ⊦ ((_∃(λ r0, r1. r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1)) * P))(H)

Rule argument

spec: <toplevel> name: tr-rec seq: ⊦ tr(r, branch(t0, a, t1)) = _∃ (λ r0, r1. r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1)) subst: [t1, a, t0, r] → [t1, a, t0, r] flags: <all paths>

Additional information

Used terms: t1, a, t0, r