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Proof step 26 from proof validrefs-put-array-badindex (previous step)

refs0 = r2 + refs, 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, (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r2 = st[r0 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', val])) ↔ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r2 = st[r0 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st)), refs0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
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, (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r2 = st[r0 -- fs '] .refval ∧ validrefs(str, st[r0 -- fs '] .refval ' + refs, fs .type, st[r -- i ', val])) ↔ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r2 = st[r0 -- fs '] .refval ∧ validrefs(str, st[r0 -- fs '] .refval ' + refs, fs .type, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, e-01, ⊦ r ' + refs ≠ []], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]