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Proof step 13 from proof unchanged-fits (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
is_array(str, r, st), fits(st[r -- sk] .refval, sks0, st), is_referencevalue(st[r -- sk]), unchanged(str, r, st, st0), unchanged(str, st[r -- sk] .refval, st, st0), junkref(str, st[r -- sk] .refval, st), is_arraytype(st[r -- _type] .type), is_indexkey(sk), sk .index < st[r -- _length] .intval, 0 ≤ sk .index, 0 < st[r -- _length] .intval ⊦ r = jvmref, ∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st)), fits(st0[r -- sk] .refval, sks0, st0) ∧ (is_arraytype(st0[r -- _type] .type) → ¬ st0[r -- _length] .intval ≤ sk .index) ∧ ¬ is_classtype(st0[r -- _type] .type) ∧ is_referencevalue(st0[r -- sk])

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, , instfields-index-01, ⊦ is_indexkey(sk) → ¬ sk ∈ instfields(class)], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPNAMEDSEQ : storekey, , test-02, ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [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 : addfuns, , isarray-isobj-01, ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)])]]