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Proof step 15 from proof abs-log-gcrash-down (previous step)

(∅)[lnum] = groupblock(gndx0, lax0, m0), (∅)[lnum] = groupblock(gndx, lax, m), ginval ∩ elems nx1 = ∅, inv(gstore \ ginval), ∀ 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, lnum ∈ gstore, lnum ∈ gstore ↓

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
(∅)[lnum] = groupblock(gndx, lax, m), ginval ∩ elems nx1 = ∅, inv(gstore \ ginval), ∀ ginval, gstore, gstore0, nx0. elems nx1 ∩ ginval = ∅ ∧ inv(gstore \ ginval) → abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx1, gstore ↓) ⊦ abs-log(nx1, crash(gstore, gstore0, ginval, nx0) ↓) = abs-log(nx1, gstore ↓), lnum ∈ ginval, lnum ∈ gstore

Rule argument

Additional information

Used simplifier rules: down-store-in: ⊦ n ∈ gstore ↓ ↔ n ∈ gstore;%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + ax0 = ax + ax1 ↔ ax0 = ax1; (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)