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Proof step 38 from proof validrefs-levelsubset-01 (previous step)

st[r -- i '] = refval(r0), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), is_array(str0, r, st), level⊆(str, str0), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str0, r0 ' + refs, st[r -- _type] .type .type, st), ∀ str1, str2, ty1, st0, ty2. level⊆(str1, str2) ∧ validrefs(str2, r0 ' + refs, ty1, st0) ∧ validref(str1, r0, ty2, st0) → validrefs(str1, r0 ' + refs, ty1, st0), i < 0 ∨ st[r -- _length] .intval ≤ i ∨ ¬ is_referencevalue(st[r -- i ']) ∨ st[r -- i '] .refval = jvmref ∨ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ validref(str, st[r -- i '] .refval, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 37:
st[r -- i '] = refval(r0), validrefs(str0, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_array(str0, r, st), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ st[r -- _type] .type .type, validref(str, r0, st[r -- _type] .type .type, st), ∀ str1, str2, ty1, st0, ty2. level⊆(str1, str2) ∧ validrefs(str2, r0 ' + refs, ty1, st0) ∧ validref(str1, r0, ty2, st0) → validrefs(str1, r0 ' + refs, ty1, st0) ⊦ r = jvmref, r0 = jvmref, validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : int-abs, , lels-03, ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]