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Proof step 39 from proof exvalidrefs-03 (previous step)

r ∈ refs0 → (∃ refs2, refs1. refs0 = refs2 + r ' + refs1 ∧ ¬ r ∈ refs2), st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ ty, is_classtype(st[r -- _type] .type), is_obj(str, r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ty ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ mkclasstype(class), is_obj(str, r0, st), junkrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st -- r), st[r0 -- _type] .type ≤ mkclasstype(class), r ∈ refs0, ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r0 = jvmref, r = jvmref, r = r0, junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), is_obj(str, r0, st), st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), st[r0 -- _type] .type ≤ ty, st[r0 -- _type] .type ≤ mkclasstype(class), junkrefs(str, (r0 ' + refs) + r ', st[r0 -- _type] .type, st -- r), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = r0, r = jvmref, r0 = jvmref, r ∈ refs, junkref(str, r0, st), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ junkrefs (str, refs + r ' + refs0, ty, st -- r) ↔ junkrefs (str, refs + r ', ty, st -- r)], [CSIMPSEQ : ⊦ refs = refs0 + r ' + refs1 → r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]