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Proof step 30 from proof validrefs-put-array-badindex (previous step)

is_obj(str, r0, st[r -- i ', val]) ∧ (st[r -- i ', val][r0 -- _type]) .type ≤ ty, is_obj(str, r0, st), i < 0, st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ refs0 = [] ∨ (∃ fs. fs ' ∈ instfields((st[r -- i ', val][r0 -- _type]) .type .class) ∧ is_referencevalue(st[r -- i ', val][r0 -- fs ']) ∧ refs0 .first = (st[r -- i ', val][r0 -- fs ']) .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', val])) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
i < 0, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ r0 = jvmref, refs0 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ refs0 .first = st[r0 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', val])) ↔ validrefs(str, r0 ' + refs0, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , is_obj-put-index, ⊦ is_obj (str, r, st[r0 -- i ', val]) ↔ is_obj(str, r, st)], [CSIMPNAMEDSEQ : javastore, , at-other, ⊦ (st[r -- i ', val] [r0 -- fs ' ] ) = st[r0 -- fs ']], [CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]])]]