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Proof step 8 from proof same-put (previous step)

str ' ∈ tree, p0 ∈ tree[str '], ∀ tree, tree0, tree1. p0 ∈ tree → tree[p0, tree0][p0, tree1] = tree[p0, tree1] ⊦ tree[str ', tree[str '][p0, tree0]][str ' + p0, tree1] = tree[str ', tree[str '][p0, tree1]]

User applied rule constructor cut

And obtained the following new goals

Proof step 9:
tree = dnode(md, sdt), p0 ∈ tree[str '], str ' ∈ tree, ∀ tree, tree0, tree1. p0 ∈ tree → tree[p0, tree0][p0, tree1] = tree[p0, tree1] ⊦ tree[str ', tree[str '][p0, tree0]][str ' + p0, tree1] = tree[str ', tree[str '][p0, tree1]]
Proof step 19:
⊦ str ' ∈ fnode(fid) ↔ false

Rule argument

var: tree

Additional information

Used simplifier rules: one-inf: ⊦ str ' ∈ fnode(fid) ↔ false;%directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;