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Proof step 36 from proof validrefs-contains-null (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
(acc + jvmref ') .first = st[r -- i '] .refval, is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc + jvmref ' + refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, acc + jvmref ', ty, st) ∧ refs0 = [] ⊦ r = jvmref, validrefs(str, (r ' + acc) + jvmref ', ty, st) ∧ refs0 = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (refs + r ' + refs0) .first = (refs + r ') .first], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]