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Proof step 10 from proof prepost-encode-group-nodes (previous step)

ax0 = [], buf2 = mkbuf(gndx.flashsize), err = ESUCCESS, err0 = ESUCCESS, m1 = m, m2 = n1, m3 = 0, m4 = 0, n = n0, m1 < # gndx, m1 ≤ # gndx, err = ESUCCESS → # buf = # buf2 ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false))), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪let m = ? in {encode_group_node#(gndx[m1], m0; m, buf; err); ax := ax + @(m2, n + m0, m); m0 := m0 + m}; m1 := m1 + 1⟫ ( ( m1 ≤ # gndx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = # buf2 ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false))))) ∧ # gndx - m1 < # gndx - m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# gndx0 = # lax, # buf0 = gndx0.flashsize, # buf1 = gndx1.flashsize, # lax + # gndx1 ≠ 0, gndx1 ≠ [], abs-nodes(buf0, n, gndx0, lax, false) ⊦ ⟪let m3 = ? in {buf := buf0 + buf1; encode_group_node#((gndx0 + gndx1)[# lax], gndx0.flashsize; m3, buf; err); ax := lax.to-adr(m2) + @(m2, n + gndx0.flashsize, m3) '; m0 := gndx0.flashsize + m3}; m1 := # gndx0 + 1⟫ ( m1 ≤ # gndx0 + # gndx1 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = gndx0.flashsize + gndx1.flashsize ∧ (∃ gndx2, gndx3. gndx0 + gndx1 = gndx2 + gndx3 ∧ # gndx2 = m1 ∧ m0 = gndx2.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = gndx2.flashsize ∧ abs-nodes(buf0, n, gndx2, lax, false)))) ∧ # gndx0 + # gndx1 - m1 < # gndx1)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%abs-nodes-elems-adr-length-h: ⊦ abs-nodes(buf, m, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]%n0 ≤ n ⊦ m < n - n0 ↔ m + n0 < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ ax + adr = ax + adr '; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ (gndx + gndx0).flashsize = gndx.flashsize + gndx0.flashsize; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m < n → m ≤ n; (s)