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Proof step 15 from proof tr-fold (conclusion)

⊦ (r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H) ↔ (tr(r, branch(t0, a, t1)) * P)(H) ∧ True(H[r] = mknode(r0, a, r1))

User applied rule case distinction

And obtained the following new goals

Proof step 8:
(r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H) ⊦ (tr(r, branch(t0, a, t1)) * P)(H) ∧ True(H[r] = mknode(r0, a, r1))
Proof step 14:
(tr(r, branch(t0, a, t1)) * P)(H) ∧ True(H[r] = mknode(r0, a, r1)) ⊦ (r => mknode(r0, a, r1) * tr(r0, t0) * tr(r1, t1) * P)(H)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]