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Proof step 125 from proof pathex-put-pathex-array-refval (conclusion)

⊦ path∃(str, r, r1, st[r0 -- sk, val]) ∧ path∃(str, r, r0, st) ∧ ¬ path∃(str, val .refval, r1, st) ∧ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval ∧ is_referencevalue(val) ∧ validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type)) → path∃(str, r, r1, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 124:
path∃(str, r, r1, st[r0 -- sk, val]), path∃(str, r, r0, st), is_indexkey(sk), sk .index < st[r0 -- _length] .intval, is_referencevalue(val), validref(str, val .refval, st[r0 -- _type] .type .type, st), is_arraytype(st[r0 -- _type] .type), 0 ≤ sk .index, 0 < st[r0 -- _length] .intval, val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type) ⊦ r0 = jvmref, path∃(str, r, r1, st), path∃(str, val .refval, r1, st)

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])]]