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Proof step 65 from proof validrefs-put-badclassfield (previous step)

r -- _length ≠ r0 -- fs ', st[r0 -- _type] .type = mkclasstype(class), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val]), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, is_array(str, r, st), ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0) ∧ ¬ junkref(str0, st[r -- i '] .refval, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, r = jvmref, dups((st[r -- i '] .refval ' + refs) .butlast), r ∈ (st[r -- i '] .refval ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), validrefs(str, r ' + st[r -- i '] .refval ' + refs, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val]), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0) ∧ ¬ junkref(str0, st[r -- i '] .refval, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, r = jvmref, r = r0, dups((st[r -- i '] .refval ' + refs) .butlast), r ∈ (st[r -- i '] .refval ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), validrefs(str, r ' + st[r -- i '] .refval ' + refs, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ is_array(str, r, st) → st[r -- _type] .type ≠ mkclasstype(class)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]