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Proof step 42 from proof tree-ext (previous step)

∀ str. str ∈ sdt → (∀ tree2. (∀ p. (p ∈ sdt[str] ↔ p ∈ tree2) ∧ ( p ∈ sdt[str] → (sdt[str][p].dir? ↔ tree2[p].dir?) ∧ (sdt[str][p].dir? ⊃ sdt[str][p].meta = tree2[p].meta;sdt[str][p].fid = tree2[p].fid))) → sdt[str] = tree2), ∀ p. (p ∈ dnode(md, sdt) → p = ε) ∧ ( p ∈ dnode(md, sdt) → (dnode(md, sdt)[p].dir? ↔ fnode(fid)[p].dir?) ∧ (dnode(md, sdt)[p].dir? ⊃ dnode(md, sdt)[p].meta = fnode(fid)[p].meta;dnode(md, sdt)[p].fid = fnode(fid)[p].fid)) ⊦

User applied rule all left

And obtained the following new goals

Rule argument

pos: left 2 terms: ε abort: F discard: F computed: T

Additional information

Used simplifier rules: nil-in: ⊦ ε ∈ tree;%nil-at: ⊦ tree[ε] = tree;%isdnode: ⊦ dnode(md, sdt).dir?;%isfnode: ⊦ ¬ fnode(fid).dir?; Used terms: ε