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Proof step 69 from proof ex-fits-validrefs-stronger (previous step)

is_array(str, r, st), st[r -- sk] = refval(r0), # refs = # sks0, fits(r0, sks0, st), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class), is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1] ⊦ validrefs(str, r ' + r0 ' + refs, st[r -- _type] .type, st), r = jvmref, junkref(str, r0, st), junkref(str, r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
st[r -- sk] = refval(r0), # refs = # sks0, is_array(str, r, st), fits(r0, sks0, st), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), is_arraytype(st[r -- _type] .type), is_indexkey(sk), sk .index < st[r -- _length] .intval, 0 ≤ sk .index, 0 < st[r -- _length] .intval, ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1] ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs, st[r -- _type] .type, st), junkref(str, r0, st), junkref(str, r, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)])]]