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Proof step 62 from proof validrefs-put-notin-01 (previous step)

is_array(str, r1, st[r -- mkfs(class, ty1, fieldvar) ', val]) ∧ (st[r -- mkfs(class, ty1, fieldvar) ', val][r1 -- _type]) .type ≤ ty, acc + r0 ' = r4 ' + refs, st[r1 -- _type] .type ≤ ty, okval(val, ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r ∈ st, is_array(str, r1, st), ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ r = r1, r1 = jvmref, mkfs(class, ty1, fieldvar) ' = _length, mkfs(class, ty1, fieldvar) ' = _type, acc + r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < (st[r -- mkfs(class, ty1, fieldvar) ', val][r1 -- _length]) .intval ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ', val][r1 -- i ']) ∧ (acc + r0 ') .first = (st[r -- mkfs(class, ty1, fieldvar) ', val][r1 -- i ']) .refval ∧ validrefs(str, acc + r0 ', (st[r -- mkfs(class, ty1, fieldvar) ', val][r1 -- _type]) .type .type, st[r -- mkfs(class, ty1, fieldvar) ', val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r4 = st[r1 -- i '] .refval ∧ validrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st)), r ∈ acc, r0 ≠ r4 ∧ ¬ r0 ∈ refs, ¬ r4 ∈ acc ∧ r4 ≠ r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
acc + r0 ' = r4 ' + refs, is_array(str, r1, st), r ∈ st, okval(st[r -- mkfs(class, ty1, fieldvar) '], ty1), r -- mkfs(class, ty1, fieldvar) ' ∈ st, okval(val, ty1), st[r1 -- _type] .type ≤ ty, ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ mkfs(class, ty1, fieldvar) ' = _type, mkfs(class, ty1, fieldvar) ' = _length, r1 = jvmref, r = r1, (∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ r4 = st[r1 -- i '] .refval ∧ validrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty1, fieldvar) ', val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r4 = st[r1 -- i '] .refval ∧ validrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st)), r ∈ acc, ¬ r4 ∈ acc ∧ r4 ≠ r0, r0 ≠ r4 ∧ ¬ r0 ∈ refs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ fs ' ≠ _length ∧ fs ' ≠ _type → ( is_array (str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]