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Proof step 58 from proof at-mod (previous step)

sdt[str][p0] = dnode(md0, sdt0), p0 ∈ sdt[str], str ∈ sdt, q0 ∈ sdt[str][p0, dnode(md1, sdt1)], ∀ md, sdt, md0, sdt0, q, md1, sdt1. dnode(md, sdt)[p0] = dnode(md0, sdt0) ∧ p0 ∈ dnode(md, sdt) ∧ q ∈ dnode(md, sdt)[p0, dnode(md1, sdt1)] → dnode(md, sdt)[p0, dnode(md1, sdt1)][q] = (q ⊑ p0 ⊃ dnode(md, sdt)[q][restn(# q, p0), dnode(md1, sdt1)];dnode(md, sdt)[p0, dnode(md0, sdt1)][q]) ⊦ sdt[str][p0, dnode(md1, sdt1)][q0] = (q0 ⊑ p0 ⊃ sdt[str][q0][restn(# q0, p0), dnode(md1, sdt1)];sdt[str][p0, dnode(md0, sdt1)][q0]), p0 = ε

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 59:
⊦ str ∈ sdt ↔ (∃ tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0)
Proof step 60:
sdt[str][p0] = dnode(md0, sdt0), q0 ∈ sdt[str][p0, dnode(md1, sdt1)], p0 ∈ sdt[str], ∀ md, sdt, md0, sdt0, q, md1, sdt1. dnode(md, sdt)[p0] = dnode(md0, sdt0) ∧ p0 ∈ dnode(md, sdt) ∧ q ∈ dnode(md, sdt)[p0, dnode(md1, sdt1)] → dnode(md, sdt)[p0, dnode(md1, sdt1)][q] = (q ⊑ p0 ⊃ dnode(md, sdt)[q][restn(# q, p0), dnode(md1, sdt1)];dnode(md, sdt)[p0, dnode(md0, sdt1)][q]), ∃ tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0 ⊦ sdt[str][p0, dnode(md1, sdt1)][q0] = (q0 ⊑ p0 ⊃ sdt[str][q0][restn(# q0, p0), dnode(md1, sdt1)];sdt[str][p0, dnode(md0, sdt1)][q0]), p0 = ε

Rule argument

spec: store, inst: directory-tree-inst name: exin seq: ⊦ str ∈ sdt ↔ (∃ tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0) subst: [sdt, str] → [sdt, str] flags: <all paths>

Additional information

Used terms: sdt, str