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Proof step 3 from proof pathex-def-simple (previous step)

validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = (refs .first ' + refs1) .last ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule exists right

And obtained the following new goals

Proof step 2:
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

[EXRARG : pos: right 1, [extquanttermlist: (r ' + refs1) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])], [EXTRATERMS : (r ' + refs1)]]