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Proof step 27 from proof validrefs-subset-01 (previous step)

acc = r + refs, r = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval, st0[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st ⊆ st0, st[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, acc, ty1, st), ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, acc, ty0, st2) ⊦ r0 = jvmref, acc = [], junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st0[r0 -- _type] .type .class) ∧ is_referencevalue(st0[r0 -- fs ']) ∧ r = st0[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
st0[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st ⊆ st0, st[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st), ∀ str0, ty0, st1, st2. validrefs(str0, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval, st1) → validrefs(str0, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st0[r0 -- _type] .type .class) ∧ is_referencevalue(st0[r0 -- fs ']) ∧ st[r0 -- mkfs(class, ty1, fieldvar) '] .refval = st0[r0 -- fs '] .refval ∧ validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, fs .type, st0)

Rule argument

[emptyarg]

Additional information

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