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Proof step 2 from proof crash-update-reverted (previous step)

gstore[n] = groupblock(gndx, lax, m0), n ∈ gstore ⊦ crash(gstore[n, groupblock(gndx, lax, m2)], gstore1, ginval, nx) = crash(gstore, gstore1, ginval, nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ gstore = gstore0 ↔ (∀ n. (n ∈ gstore ↔ n ∈ gstore0) ∧ (n ∈ gstore → gstore[n] = gstore0[n]))
Proof step 4:
gstore[n] = groupblock(gndx, lax, m0), n ∈ gstore ⊦ ∀ n0. (n0 ∈ crash(gstore[n, groupblock(gndx, lax, m2)], gstore1, ginval, nx) ↔ n0 ∈ crash(gstore, gstore1, ginval, nx)) ∧ ( n0 ∈ crash(gstore[n, groupblock(gndx, lax, m2)], gstore1, ginval, nx) → crash(gstore[n, groupblock(gndx, lax, m2)], gstore1, ginval, nx)[n0] = crash(gstore, gstore1, ginval, nx)[n0])

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: k-Extension seq: ⊦ gstore = gstore0 ↔ (∀ n. (n ∈ gstore ↔ n ∈ gstore0) ∧ (n ∈ gstore → gstore[n] = gstore0[n])) subst: [gstore0, gstore] → [crash(gstore, gstore1, ginval, nx), crash (gstore[n, groupblock(gndx, lax, m2)], gstore1, ginval, nx)] flags: <all paths>

Additional information

Used terms: crash(gstore, gstore1, ginval, nx), crash(gstore[n, groupblock(gndx, lax, m2)], gstore1, ginval, nx)