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Proof step 63 from proof validrefs-put-badclassfield (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, 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), st[r -- i '] .refval ' + refs = [] ∨ (∃ i0. 0 ≤ i0 ∧ i0 < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i0 ']) ∧ (st[r -- i '] .refval ' + refs) .first = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
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), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i '] .refval = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]