| is_classtype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), ∀ str, ty, st, fs, r0, val. ¬ validrefs(str, acc, ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ fs ' ≠ _type ∧ is_classtype(st[r0 -- _type] .type) ∧ ¬ fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ acc ≠ [] ∧ ¬ dups(acc .butlast) → ¬ validrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ acc ≠ [], fs ' = _type, dups((r ' + acc) .butlast), fs ' ∈ instfields(st[r0 -- _type] .type .class), junkref(str, r, st), validrefs(str, r ' + acc, ty, st) |
⊦ validrefs(str, [], ty, st)
is_classtype(st[r0 -- _type] .type), validrefs(str, r ', ty, st[r0 -- fs ', val]) ⊦ fs ' = _type, fs ' ∈ instfields(st[r0 -- _type] .type .class), junkref(str, r, st), validrefs(str, r ', ty, st)
[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ dups([])], [CSIMPSEQ : ⊦ r ' .butlast = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + [] = refs])]]