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Proof step 67 from proof validrefs-put-badclassfield (previous step)

is_array(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st), st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, r1 ' + refs = [] ∨ (∃ i. 0 ≤ i ∧ i < (st[r0 -- fs ', val][r -- _length]) .intval ∧ is_referencevalue(st[r0 -- fs ', val][r -- i ']) ∧ (r1 ' + refs) .first = (st[r0 -- fs ', val][r -- i ']) .refval ∧ validrefs(str, r1 ' + refs, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val])), ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(str, r, st[r0 -- fs ', val]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + r1 ' + refs, ty, st), junkref(str, r, st), fs ' ∈ instfields(class), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
st[r0 -- _type] .type = mkclasstype(class), 0 < (st[r0 -- fs ', val][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[r0 -- fs ', val][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)

Rule argument

[emptyarg]

Additional information

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