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Proof step 39 from proof validrefs-put-statfield (previous step)

st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), ∀ str0, ty0, st0, sk0, val0. validrefs(str0, r0 ' + refs, ty0, st0[jvmref -- sk0, val0]) ↔ validrefs(str0, r0 ' + refs, ty0, st0) ⊦ r = jvmref, ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[jvmref -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str0, ty0, st0, sk0, val0. validrefs(str0, r0 ' + refs, ty0, st0[jvmref -- sk0, val0]) ↔ validrefs(str0, r0 ' + refs, ty0, st0) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st[jvmref -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]