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Proof step 7 from proof pathex-class (previous step)

validrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), is_valid_ref(str, st[r -- fs '] .refval, st), st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ⊦ r = (st[r -- fs '] .refval ' + refs) .last, st[r -- fs '] .refval = jvmref, ∃ refs0. refs0 ≠ [] ∧ refs0 .first = st[r -- fs '] .refval ∧ refs0 .last = (st[r -- fs '] .refval ' + refs) .last ∧ validrefs(str, refs0, st[st[r -- fs '] .refval -- _type] .type, st)

Heuristic quantifier closing applied rule exists right

And obtained the following new goals

Proof step 6:
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

[EXRARG : pos: right 3, [QUANTTERMLIST : (st[r -- fs '] .refval ' + refs)]]

Additional information

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