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Proof step 20 from proof abs-log-gcrash-down (previous step)

crash(gstore, gstore0, ginval, nx0) ↓[lnum] = groupblock(gndx, lax, m), 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) ↓) = prefixn(valid-group-nodes(gstore[lnum].gndlist), gstore[lnum].ladrlist).to-adr(lnum) + abs-log(nx1, gstore ↓), lnum ∈ ginval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
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) ↓) = prefixn(valid-group-nodes(gndx0), lax0).to-adr(lnum) + abs-log(nx1, gstore ↓), lnum ∈ ginval

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore[lnum], gndx0, lax0, m0]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore[lnum], gndx0, lax0, m0