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Proof step 15 from proof abs-gstore-reduce-write-idcircle (previous step)

# lpt = # avol0, # avol1 = # avol0, lpt[n] = mklp(m4, m5, lpf0, m6), gstore[n] = groupblock(gndx0, lax0, m3), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size), ∀ m. m < # avol0 ∧ m ≠ n → avol1[m] = avol0[m], ∀ n0. (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore[n, groupblock(gndx, lax, m)]) ∧ ( n0 ∈ gstore[n, groupblock(gndx, lax, m)] ∧ ¬ n0 ∈ ginval → abs-leb(avol1[n0], gstore[n, groupblock(gndx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0])) ∧ (n0 ∈ gstore[n, groupblock(gndx, lax, m)] → lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = gstore[n, groupblock(gndx, lax, m)][n0].ref-size) ⊦ n < # avol0 ∧ ((lpf0 = LP_GROUP_NODES → m4 = m3) → m0 = m ∧ lpf = LP_GROUP_NODES) ∧ ( ¬ n ∈ ginval ∧ (lpf0 = LP_GROUP_NODES → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, LP_GROUP_NODES, m6))) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2)))

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: n abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ n ∈ gstore[n, gblock]; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ groupblock(gndx, lax, m).ref-size = m; (s) Used terms: n