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Proof step 3 from proof path-uni-com (previous step)

ispath(p, n0, n1, dirs1, files), dirs0 ⊥ dirs1 ⊦ ispath(p, n0, n1, dirs0 ∪ dirs1, files)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ dirs ⊥ dirs0 → dirs0 ∪ dirs = dirs ∪ dirs0
Proof step 5:
ispath(p, n0, n1, dirs1, files), dirs0 ⊥ dirs1, dirs1 ⊥ dirs0 ⊦ ispath(p, n0, n1, dirs1 ∪ dirs0, files)

Rule argument

spec: heap, inst: dir-heap name: uni-com seq: ⊦ dirs ⊥ dirs0 → dirs0 ∪ dirs = dirs ∪ dirs0 subst: [dirs, dirs0] → [dirs1, dirs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ dirs ⊥ dirs0 → dirs0 ⊥ dirs; (s) Used terms: dirs1, dirs0