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Proof step 32 from proof validrefs-set-null (previous step)

acc .first = st[r -- fs0 '] .refval, is_reftype(fs .type), st[r -- _type] .type ≤ ty, fs0 ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs0 ']), validrefs(str, acc + refs0, fs0 .type, st), is_obj(str, r, st[acc .last -- fs ', refval(jvmref)]), (st[acc .last -- fs ', refval(jvmref)][r -- _type]) .type ≤ ty, is_obj(str, r, st), fs ' ∈ instfields(st[acc .last -- _type] .type .class), is_obj(str, acc .last, st), ∀ str0, refs, ty0, st0, fs1. validrefs(str0, acc + refs, ty0, st0) ∧ is_obj(str0, acc .last, st0) ∧ fs1 ' ∈ instfields(st0[acc .last -- _type] .type .class) ∧ is_reftype(fs1 .type) ∧ refs ≠ [] → validrefs(str0, acc + jvmref ', ty0, st0[acc .last -- fs1 ', refval(jvmref)]) ⊦ acc = [], r = jvmref, refs0 = [], r ∈ acc, dups(acc), ∃ fs1. fs1 ' ∈ instfields((st[acc .last -- fs ', refval(jvmref)][r -- _type]) .type .class) ∧ is_referencevalue(st[acc .last -- fs ', refval(jvmref)][r -- fs1 ']) ∧ acc .first = (st[acc .last -- fs ', refval(jvmref)][r -- fs1 ']) .refval ∧ validrefs(str, acc + jvmref ', fs1 .type, st[acc .last -- fs ', refval(jvmref)])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 31:
acc .first = st[r -- fs0 '] .refval, is_reftype(fs .type), st[r -- _type] .type ≤ ty, fs0 ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs0 ']), validrefs(str, acc + refs0, fs0 .type, st), is_obj(str, r, st[acc .last -- fs ', refval(jvmref)]), (st[acc .last -- fs ', refval(jvmref)][r -- _type]) .type ≤ ty, is_obj(str, r, st), fs ' ∈ instfields(st[acc .last -- _type] .type .class), is_obj(str, acc .last, st), ∀ str0, refs, ty0, st0, fs1. validrefs(str0, acc + refs, ty0, st0) ∧ is_obj(str0, acc .last, st0) ∧ fs1 ' ∈ instfields(st0[acc .last -- _type] .type .class) ∧ is_reftype(fs1 .type) ∧ refs ≠ [] → validrefs(str0, acc + jvmref ', ty0, st0[acc .last -- fs1 ', refval(jvmref)]) ⊦ r -- _type = acc .last -- fs ', acc = [], r = jvmref, refs0 = [], r ∈ acc, dups(acc), ∃ fs1. fs1 ' ∈ instfields((st[acc .last -- fs ', refval(jvmref)][r -- _type]) .type .class) ∧ is_referencevalue(st[acc .last -- fs ', refval(jvmref)][r -- fs1 ']) ∧ acc .first = (st[acc .last -- fs ', refval(jvmref)][r -- fs1 ']) .refval ∧ validrefs(str, acc + jvmref ', fs1 .type, st[acc .last -- fs ', refval(jvmref)])

Rule argument

[fma-arg: r -- _type = acc .last -- fs ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ refs .last = r ∧ refs ≠ [] → r ∈ refs])], [EXTRAFMAS : (r -- _type = acc .last -- fs ')]]