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Proof step 31 from proof validrefs-put-array-badindex (previous step)

is_obj(str, r0, st), i < 0, st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 30:
is_obj(str, r0, st[r -- i ', val]) ∧ (st[r -- i ', val][r0 -- _type]) .type ≤ ty, is_obj(str, r0, st), i < 0, st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ refs0 = [] ∨ (∃ fs. fs ' ∈ instfields((st[r -- i ', val][r0 -- _type]) .type .class) ∧ is_referencevalue(st[r -- i ', val][r0 -- fs ']) ∧ refs0 .first = (st[r -- i ', val][r0 -- fs ']) .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', val])) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-class antecedent: succedent: is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st))) substlist: [st, ty, refs, r, str] → [st[r -- i ', val], ty, refs0, r0, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , is_obj-put-index, ⊦ is_obj (str, r, st[r0 -- i ', val]) ↔ is_obj(str, r, st)], [CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]])], [EXTRATERMS : (st[r -- i ', val], ty, refs0, r0, str)]]