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Proof step 24 from proof in-mod (previous step)

sdt0[str] = dnode(md0, sdt), str0 ∈ sdt0[str, dnode(md1, sdt)], str ∈ sdt0 ⊦ q0 ∈ sdt0[str, dnode(md1, sdt)][str0] ↔ str0 ∈ sdt0 ∧ q0 ∈ sdt0[str0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ str ≠ str0 → sdt[str0, tree][str] = sdt[str]
Proof step 26:
sdt0[str] = dnode(md0, sdt), str0 = str, str ∈ sdt0, str0 ∈ sdt0[str, dnode(md1, sdt)] ⊦ q0 ∈ sdt0[str, dnode(md1, sdt)][str0] ↔ str0 ∈ sdt0 ∧ q0 ∈ sdt0[str0]

Rule argument

spec: store, inst: directory-tree-inst name: At-other seq: ⊦ str ≠ str0 → sdt[str0, tree][str] = sdt[str] subst: [str, tree, str0, sdt] → [str0, dnode(md1, sdt), str, sdt0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ str ∈ sdt → sdt[str] = (∅)[str]; (s)% ⊦ str ∈ sdt[str0, tree] ↔ str = str0 ∨ str ∈ sdt; (ws) Used terms: str0, dnode(md1, sdt), str, sdt0