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Proof step 16 from proof validrefs-set-null (previous step)

refs0 .first = st[r -- fs0 '] .refval, validrefs(str, refs0, fs0 .type, st), is_referencevalue(st[r -- fs0 ']), fs0 ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_reftype(fs .type), is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class) ⊦ r -- _type = r -- fs ', refs0 = [], r = jvmref, validrefs(str, r ' + jvmref ', ty, st[r -- fs ', refval(jvmref)]), is_obj(str, r, st[r -- fs ', refval(jvmref)]) ∧ (st[r -- fs ', refval(jvmref)][r -- _type]) .type ≤ ty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
refs0 .first = st[r -- fs0 '] .refval, validrefs(str, refs0, fs0 .type, st), is_referencevalue(st[r -- fs0 ']), fs0 ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_reftype(fs .type), is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class) ⊦ refs0 = [], r = jvmref, _type = fs ', validrefs(str, r ' + jvmref ', ty, st[r -- fs ', refval(jvmref)]), is_obj(str, r, st[r -- fs ', refval(jvmref)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]