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Proof step 9 from proof pathex-subset (previous step)

refs = r + refs0, st ⊆ st0, validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st), validref(str, r, ty, st) ⊦ refs = [], path∃(str, r, refs .last, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
validref(str, r, ty, st), st ⊆ st0, validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ path∃(str, r, (r ' + refs0) .last, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]