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Proof step 13 from proof crash-update-reverted (previous step)

gstore[n] = groupblock(gndx, lax, m0), n ∈ gstore, n0 ∈ gstore ∨ n0 ∈ ginval ⊦ (n0 ∈ nx ∨ ¬ n0 ∈ ginval ⊃ groupblock (gstore[n, groupblock(gndx, lax, m2)][n0].gndlist, gstore[n, groupblock(gndx, lax, m2)][n0].ladrlist, (n0 ∈ gstore1 ⊃ gstore1[n0].ref-size;0)) ;gstore1[n0] ) = crash(gstore, gstore1, ginval, nx)[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ n ∈ crash(gstore, gstore0, ginval, nx) → crash(gstore, gstore0, ginval, nx)[n] = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n])
Proof step 15:
gstore[n] = groupblock(gndx, lax, m0), n ∈ gstore, n0 ∈ crash(gstore, gstore1, ginval, nx), n0 ∈ gstore ∨ n0 ∈ ginval ⊦ (n0 ∈ nx ∨ ¬ n0 ∈ ginval ⊃ groupblock (gstore[n, groupblock(gndx, lax, m2)][n0].gndlist, gstore[n, groupblock(gndx, lax, m2)][n0].ladrlist, (n0 ∈ gstore1 ⊃ gstore1[n0].ref-size;0)) ;gstore1[n0] ) = (n0 ∈ nx ∨ ¬ n0 ∈ ginval ⊃ groupblock(gstore[n0].gndlist, gstore[n0].ladrlist, (n0 ∈ gstore1 ⊃ gstore1[n0].ref-size;0));gstore1[n0])

Rule argument

spec: <toplevel> name: crash-group-at seq: ⊦ n ∈ crash(gstore, gstore0, ginval, nx) → crash(gstore, gstore0, ginval, nx)[n] = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock (gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)) ;gstore0[n] ) subst: [n, nx, ginval, gstore0, gstore] → [n0, nx, ginval, gstore1, gstore] flags: <all paths>

Additional information

Used simplifier rules: crash-group-in: ⊦ n ∈ crash(gstore, gstore0, ginval, nx) ↔ n ∈ gstore ∨ n ∈ ginval;% ⊦ ¬ n ∈ gstore → gstore[n] = (∅)[n]; (s) Used terms: n0, nx, ginval, gstore1, gstore