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Proof step 15 from proof icrash-remove-refsize0-prefix (previous step)

istore0[n] = indexblock(indx, lax, m), crash(istore, istore0)[n] = indexblock(indx0, lax0, m0), n ∈ istore, n ∈ istore0, dom istore0 ⊆ dom istore, ∀ n. n ∈ istore0 ∧ n ∈ istore → istore0[n].indlist ⊑ istore[n].indlist ∧ istore0[n].ladrlist ⊑ istore[n].ladrlist ∧ # istore0[n].indlist = # istore0[n].ladrlist ∧ # istore[n].indlist = # istore[n].ladrlist, ∀ n. (n ∈ istore0 ↔ n ∈ remove-refsize0(istore0)) ∧ istore0[n] = remove-refsize0(istore0)[n] ⊦ m0 = 0, indx ⊑ indx0 ∧ lax ⊑ lax0 ∧ # indx = # lax ∧ # indx0 = # lax0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ n ∈ istore0 → crash(istore, istore0)[n] = indexblock(istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size)
Proof step 17:
istore0[n] = indexblock(indx, lax, m), indexblock(istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size) = indexblock(indx0, lax0, m0), n ∈ istore, n ∈ istore0, dom istore0 ⊆ dom istore, ∀ n. (n ∈ istore0 ↔ n ∈ remove-refsize0(istore0)) ∧ istore0[n] = remove-refsize0(istore0)[n], ∀ n. n ∈ istore0 ∧ n ∈ istore → istore0[n].indlist ⊑ istore[n].indlist ∧ istore0[n].ladrlist ⊑ istore[n].ladrlist ∧ # istore0[n].indlist = # istore0[n].ladrlist ∧ # istore[n].indlist = # istore[n].ladrlist ⊦ m0 = 0, indx ⊑ indx0 ∧ lax ⊑ lax0 ∧ # indx = # lax ∧ # indx0 = # lax0

Rule argument

spec: <toplevel> name: crash-index-at seq: ⊦ n ∈ istore0 → crash(istore, istore0)[n] = indexblock (istore[n].indlist, istore[n].ladrlist, istore0[n].ref-size) subst: [n, istore0, istore] → [n, istore0, istore] flags: <all paths>

Additional information

Used terms: n, istore0, istore