[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 18 from proof at-mod (previous step)

sdt[str][p0] = dnode(md0, sdt0), str ∈ sdt, p0 ∈ sdt[str], q ∈ dnode(md, 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]) ⊦ dnode(md, sdt)[str ' + p0, dnode(md1, sdt1)][q] = (q ⊑ str ' + p0 ⊃ dnode(md, sdt)[q][restn(# q, str ' + p0), dnode(md1, sdt1)];dnode(md, sdt)[str ' + p0, dnode(md0, sdt1)][q])

User applied rule constructor cut

And obtained the following new goals

Proof step 19:
⊦ tree[ε] = tree
Proof step 20:
sdt[str][p0] = dnode(md0, sdt0), q = str0 + q0, q ∈ dnode(md, sdt)[str ' + p0, dnode(md1, sdt1)], p0 ∈ sdt[str], str ∈ sdt, ∀ 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]) ⊦ dnode(md, sdt)[str ' + p0, dnode(md1, sdt1)][q] = (q ⊑ str ' + p0 ⊃ dnode(md, sdt)[q][restn(# q, str ' + p0), dnode(md1, sdt1)];dnode(md, sdt)[str ' + p0, dnode(md0, sdt1)][q])

Rule argument

var: q

Additional information

Used simplifier rules: nil-at: ⊦ tree[ε] = tree;%path freely generated by ε, +;;% ⊦ ε ⊑ p; (s)% ⊦ # ε = 0; (s)% ⊦ restn(0, p) = p; (s)