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Proof step 18 from proof validrefs-set-null (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
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, 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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ dups([])], [CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ [] + refs = refs])]]