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Proof step 12 from proof abs-gstore-set-refsize (previous step)

n5 < # lpt ∧ lpf0 = LP_GROUP_NODES ↔ n5 ∈ gstore, lpt[n5] = mklp(m5, m6, lpf0, m7), gstore[n5] = groupblock(gndx1, lax1, m4), gstore[n] = groupblock(gndx, lax, n3), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n4), gstore[n, groupblock(gndx, lax, m0)][n5] = groupblock(gndx0, lax0, m), lpt[n, mklp(m0, n1, LP_GROUP_NODES, n2)][n5] = mklp(m1, m2, lpf, m3), n ∈ gstore, n5 ∈ gstore ∧ ¬ n5 ∈ ginval → abs-leb(avol[n5], groupblock(gndx1, lax1, m4), mklp(m5, m6, lpf0, m7)), n5 ∈ gstore → m5 = m4 ⊦ (n5 < # lpt ∧ lpf = LP_GROUP_NODES ↔ n5 ∈ gstore[n, groupblock(gndx, lax, m0)]) ∧ (n5 ∈ gstore[n, groupblock(gndx, lax, m0)] ∧ ¬ n5 ∈ ginval → abs-leb(avol[n5], groupblock(gndx0, lax0, m), mklp(m1, m2, lpf, m3))) ∧ (n5 ∈ gstore[n, groupblock(gndx, lax, m0)] → m1 = m)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: group-store-ablock-store-nat-store name: At-other seq: ⊦ n ≠ n0 → gstore[n0, gblock][n] = gstore[n] subst: [n, gblock, n0, gstore] → [n5, groupblock(gndx, lax, m0), n, gstore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m]; (s)% ⊦ n ≠ n0 → (n ∈ gstore[n0, gblock] ↔ n ∈ gstore); (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws) Used terms: n5, groupblock(gndx, lax, m0), n, gstore