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Proof step 68 from proof validrefs-set-null (previous step)

∀ str, refs0, ty, st, fs. validrefs(str, acc + refs0, ty, st) ∧ ¬ dups(acc) ∧ acc ≠ [] ∧ is_obj(str, acc .last, st) ∧ fs ' ∈ instfields(st[acc .last -- _type] .type .class) ∧ is_reftype(fs .type) ∧ refs0 ≠ [] → validrefs(str, acc + jvmref ', ty, st[acc .last -- fs ', refval(jvmref)]) ⊦ validrefs(str, (r + acc) + refs0, ty, st) ∧ ¬ dups(r + acc) ∧ r + acc ≠ [] ∧ is_obj(str, (r + acc) .last, st) ∧ fs ' ∈ instfields(st[(r + acc) .last -- _type] .type .class) ∧ is_reftype(fs .type) ∧ refs0 ≠ [] → validrefs(str, (r + acc) + jvmref ', ty, st[(r + acc) .last -- fs ', refval(jvmref)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
is_reftype(fs .type), validrefs(str, (r ' + acc) + refs0, ty, st), is_obj(str, (r ' + acc) .last, st), fs ' ∈ instfields(st[(r ' + acc) .last -- _type] .type .class), ∀ str0, refs, ty0, st0, fs0. validrefs(str0, acc + refs, ty0, st0) ∧ acc ≠ [] ∧ is_obj(str0, acc .last, st0) ∧ fs0 ' ∈ instfields(st0[acc .last -- _type] .type .class) ∧ is_reftype(fs0 .type) ∧ refs ≠ [] → validrefs(str0, acc + jvmref ', ty0, st0[acc .last -- fs0 ', refval(jvmref)]) ⊦ refs0 = [], validrefs(str, (r ' + acc) + jvmref ', ty, st[(r ' + acc) .last -- fs ', refval(jvmref)]), dups(acc), r ∈ acc

Rule argument

[emptyarg]

Additional information

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