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Proof step 17 from proof abs-log-gcrash-down (previous step)

crash(gstore, gstore0, ginval, nx0) ↓[lnum] = groupblock(gndx, lax, m), gstore[lnum] ↓ = groupblock(gndx0, lax0, m0), ginval ∩ elems nx1 = ∅, inv(gstore \ ginval), lnum ∈ gstore, ∀ ginval, gstore, gstore0, nx0. elems nx1 ∩ ginval = ∅ ∧ inv(gstore \ ginval) → abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx1, gstore ↓) ⊦ lax.to-adr(lnum) + abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = lax0.to-adr(lnum) + abs-log(nx1, gstore ↓), lnum ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ gblock ↓ = groupblock (prefixn(valid-group-nodes(gblock.gndlist), gblock.gndlist), prefixn(valid-group-nodes(gblock.gndlist), gblock.ladrlist), gblock.ref-size)
Proof step 19:
crash(gstore, gstore0, ginval, nx0) ↓[lnum] = groupblock(gndx, lax, m), groupblock (prefixn(valid-group-nodes(gstore[lnum].gndlist), gstore[lnum].gndlist), prefixn(valid-group-nodes(gstore[lnum].gndlist), gstore[lnum].ladrlist), gstore[lnum].ref-size) = groupblock(gndx0, lax0, m0), ginval ∩ elems nx1 = ∅, inv(gstore \ ginval), lnum ∈ gstore, ∀ ginval, gstore, gstore0, nx0. elems nx1 ∩ ginval = ∅ ∧ inv(gstore \ ginval) → abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx1, gstore ↓) ⊦ lax.to-adr(lnum) + abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = lax0.to-adr(lnum) + abs-log(nx1, gstore ↓), lnum ∈ ginval

Rule argument

spec: <toplevel> name: down-block seq: ⊦ gblock ↓ = groupblock (prefixn(valid-group-nodes(gblock.gndlist), gblock.gndlist), prefixn(valid-group-nodes(gblock.gndlist), gblock.ladrlist), gblock.ref-size) subst: [gblock] → [gstore[lnum]] flags: <all paths>

Additional information

Used terms: gstore[lnum]