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Proof step 109 from proof exvalidrefs (previous step)

type∃(str, ty) → (ty ≤ st[r0 -- _type] .type → ty = st[r0 -- _type] .type), st[r -- mkfs(class, st[r -- _type] .type, fieldvar) '] = refval(r0), is_obj(str, r0, st), st[r0 -- _type] .type ≤ st[r -- _type] .type, is_obj(str, r, st), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ ty. type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∀ ty. type∃(str, ty) → (ty ≤ st0[r -- _type] .type ↔ ty = st0[r -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ fs .type = st0[r -- _type] .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r0 = jvmref, r = r0, r = jvmref, junkref(str, r0, st), cyclic(str, r, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st[r -- fs ']) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st)), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, ¬ junkref(str, r0, st -- r) ∧ ¬ cyclic(str, r0, st -- r) ∧ (type∃(str, ty) → (ty ≤ st[r0 -- _type] .type → ty = st[r0 -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ fs .type = st[r0 -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
st[r -- mkfs(class, st[r -- _type] .type, fieldvar) '] = refval(r0), is_obj(str, r0, st), st[r0 -- _type] .type ≤ st[r -- _type] .type, is_obj(str, r, st), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), type∃(str, ty) → (ty ≤ st[r0 -- _type] .type → ty = st[r0 -- _type] .type), ∀ ty. type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∀ ty. type∃(str, ty) → (ty ≤ st0[r -- _type] .type ↔ ty = st0[r -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ fs .type = st0[r -- _type] .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r0 = jvmref, r = r0, r = jvmref, junkref(str, r0, st), cyclic(str, r, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st[r -- fs ']) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st)), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref, ¬ junkref(str, r0, st -- r) ∧ ¬ cyclic(str, r0, st -- r) ∧ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ fs .type = st[r0 -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]