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Proof step 50 from proof unchanged-lookup-list-generic (previous step)

¬ is_obj(str, r, st0), junkref(str, st0[r -- sk] .refval, st0), unchanged(str, st0[r -- sk] .refval, st, st0), unchanged(str, r, st, st0), fits(st0[r -- sk] .refval, sks0, st0), fits(st0[r -- sk] .refval, sks0, st), is_referencevalue(st0[r -- sk]), is_valid_ref(str, r, st), is_array(str, r, st0), is_arraytype(st[r -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st0[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st0[r -- _length] .intval, is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class) ⊦ sks0 = [], st[st0[r -- sk] .refval -- sks0] = st0[st0[r -- sk] .refval -- sks0], r = jvmref, junkref(str, r, st), junkref(str, r, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
is_array(str, r, st0), is_arraytype(st0[r -- _type] .type), is_indexkey(sk), sk .index < st0[r -- _length] .intval, is_arraytype(st[r -- _type] .type), junkref(str, st0[r -- sk] .refval, st0), unchanged(str, st0[r -- sk] .refval, st, st0), unchanged(str, r, st, st0), fits(st0[r -- sk] .refval, sks0, st0), fits(st0[r -- sk] .refval, sks0, st), is_referencevalue(st0[r -- sk]), is_array(str, r, st), sk .index < st[r -- _length] .intval, 0 ≤ sk .index, 0 < st0[r -- _length] .intval, 0 < st[r -- _length] .intval ⊦ sks0 = [], st[st0[r -- sk] .refval -- sks0] = st0[st0[r -- sk] .refval -- sks0], r = jvmref, junkref(str, r, st), junkref(str, r, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDFORWARD : int-abs, , forward-le-05, ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref-array-01, ⊦ is_arraytype (st[r -- _type] .type) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPNAMEDSEQ : addfuns, , is_obj-classtype, ⊦ ¬ is_classtype (st[r -- _type] .type) → ¬ is_obj(str, r, st)], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref-no-arraytype, ⊦ ¬ is_arraytype (st[r -- _type] .type) → ( is_valid_ref(str, r, st) ↔ is_obj(str, r, st))], [CSIMPNAMEDSEQ : addfuns, , instfields-index-01, ⊦ is_indexkey(sk) → ¬ sk ∈ instfields(class)], [CSIMPNAMEDSEQ : int-abs, , zero-gels-04, ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPNAMEDSEQ : javatype, , diff-01, ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPNAMEDSEQ : okfuns, , is_array-arraytype, ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPNAMEDSEQ : okfuns, , is_array-classtype, ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPNAMEDSEQ : addfuns, , isarray-isobj-01, ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)])]]