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Proof step 12 from proof tree-ext (previous step)

∀ p. (p ∈ tree0 → p = ε) ∧ (p = ε → ¬ tree0.dir? ∧ fid = tree0.fid) ⊦ fnode(fid) = tree0

User applied rule all left

And obtained the following new goals

Rule argument

pos: left 1 terms: ε abort: F discard: T computed: T

Additional information

Used simplifier rules: fnode-elim-strong: ⊦ tree.dir? ↔ ¬(∃ fid. tree = fnode(fid));%nil-in: ⊦ ε ∈ tree;%fid: ⊦ fnode(fid).fid = fid;% ⊦ fnode(fid) = fnode(fid0) ↔ fid = fid0; (s) Used terms: ε