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Proof step 46 from proof unchNorec-validrefs (previous step)

is_array(str, r, st0) ∧ st0[r -- _type] .type ≤ ty, st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- _type] .type = mkarraytype(ty0), unchangedNorec(r, st, st0), mkarraytype(ty0) ≤ ty, is_array(str, r, st), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), refs0 = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty0, st), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st0[r -- i ']) ∧ refs0 .first = st0[r -- i '] .refval ∧ validrefs(str, refs0, st0[r -- _type] .type .type, st0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
refs0 .first = st[r -- i '] .refval, st0[r -- _type] .type = mkarraytype(ty0), st[r -- _type] = st0[r -- _type], st[r -- _length] = st0[r -- _length], 0 < st0[r -- _length] .intval, 0 ≤ i, validrefs(str, refs0, ty0, st), is_referencevalue(st[r -- i ']), i < st0[r -- _length] .intval, is_array(str, r, st), unchangedNorec(r, st, st0), mkarraytype(ty0) ≤ ty, is_array(str, r, st0), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ refs0 = [], r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st0[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st0[r -- i0 ']) ∧ refs0 .first = st0[r -- i0 '] .refval ∧ validrefs(str, refs0, ty0, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]