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Proof step 26 from proof isvalidref-put-array-badindex (previous step)

i < 0 ⊦ is_valid_ref(r0, st[r -- i ', val]) ∧ (class+∃(str, st[r0 -- _type] .type .class) ∧ ¬ is_abstract(st[r0 -- _type] .type .class) ∧ is_obj(r0, st) ∨ is_array(str, r0, st[r -- i ', val])) ↔ is_obj(str, r0, st) ∨ is_array(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ r ≠ r0 → (is_valid_ref(r0, st[r -- sk, val]) ↔ is_valid_ref(r0, st))
Proof step 22:
¬ r ≠ r0, i < 0 ⊦ is_valid_ref(r0, st[r -- i ', val]) ∧ (class+∃(str, st[r0 -- _type] .type .class) ∧ ¬ is_abstract(st[r0 -- _type] .type .class) ∧ is_obj(r0, st) ∨ is_array(str, r0, st[r -- i ', val])) ↔ is_obj(str, r0, st) ∨ is_array(str, r0, st)
Proof step 23:
⊦ is_obj(r, st) → is_valid_ref(r, st)
Proof step 24:
⊦ is_obj(str, r, st) ↔ class+∃(str, st[r -- _type] .type .class) ∧ ¬ is_abstract(st[r -- _type] .type .class) ∧ is_obj(r, st)
Proof step 25:
⊦ ¬ is_valid_ref(r, st) → ¬ is_array(str, r, st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validref-put-01 antecedent: succedent: r ≠ r0 → ( is_valid_ref(r0, st[r -- sk, val]) ↔ is_valid_ref(r0, st)) substlist: [val, sk, r, st, r0] → [val, i ', r, st, r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : okfuns, , is_array-put-01, ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))])], [EXTRATERMS : (val, i ', r, st, r0)]]