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Proof step 10 from proof validrefs-put-array-badindex (previous step)

st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r2), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), i < 0, validrefs(str, r2 ' + refs, ty1, st[r -- i ', val]), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']) ∧ r2 = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, mkfs(class, ty1, fieldvar) .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r2), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r2 ' + refs, ty1, st[r -- i ', val]), i < 0, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, validrefs(str, r2 ' + refs, ty1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : fieldspec, , sel-03, ⊦ mkfs(class, ty, fieldvar) .type = ty])]]