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Proof step 73 from proof refine-allocate-ind (previous step)

# lpt2 = # avol0, # lpt0 = # avol0, isbuf ↔ false, lpt2[n0] = mklp(0, m3, LP_FREE, m2), adr = adr0, avol = avol0[n0, mapped(mkbuf(0))], keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt0, m0 = 0, m1 = n0, ns = ns0, remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum) ⊦ ⟪if bleb = buffered(m1) ∨ (bleb = nobuffer ∨ is-aligned(# avol[bleb.leb].data, EB_PAGE_SIZE)) ∧ m1 < # avol ∧ avol[m1].mapped? ∧ m0 = # avol[m1].data then {fail_or_success#(; ; err); if err = ESUCCESS then bleb := buffered(m1)} else abort; lpt1 := lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)] [n0, lpt2[n0, mklp(lpt2[n0].ref-size, 0, lpt2[n0].flags, lpt2[n0].gcheapidx)][n0].ref-size:= 0 ]; err0 := err; if err0 ≠ ESUCCESS then freelist := n0 ' + (n0 ' + nx0).tail else lpt1[n0].flags := LP_INDEX_NODES⟫ ⟨pstate0 := pstate; apersistence_allocate_ind#(adr0, istore0, ginval, gstore, gstore0, log1, m, ns0, true; istore, pstate; err1)⟩ ( abs-istore(avol0[n0, mapped(mkbuf(0))], lpt1, istore) ∧ abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err0 = err1), pstate = readonly, dups(log1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 74:
# lpt0 = # avol0, # lpt2 = # avol0, isbuf ↔ false, lpt2[n0] = mklp(0, m3, LP_FREE, m2), lpt2[n0] = mklp(m4, m5, lpf, m6), adr = adr0, avol = avol0[n0, mapped(mkbuf(0))], keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt0, m0 = 0, m1 = n0, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol0, n0 < # avol0, abs-gstore(avol0, lpt2, gstore, ginval), abs-istore(avol0, lpt2, istore), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb, lpt2, avol0), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt2, n0 ' + nx0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), synced(avol0), istore0 ⊑ istore, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer ⊦ ⟪if bleb = buffered(m1) ∨ (bleb = nobuffer ∨ is-aligned(# avol[bleb.leb].data, EB_PAGE_SIZE)) ∧ m1 < # avol ∧ avol[m1].mapped? ∧ m0 = # avol[m1].data then {fail_or_success#(; ; err); if err = ESUCCESS then bleb := buffered(m1)} else abort; lpt1 := lpt2[n0, mklp(m4, 0, lpf, m6)][n0, lpt2[n0, mklp(m4, 0, lpf, m6)][n0].ref-size:= 0]; err0 := err; if err0 ≠ ESUCCESS then freelist := n0 ' + (n0 ' + nx0).tail else lpt1[n0].flags := LP_INDEX_NODES⟫ ⟨pstate0 := pstate; apersistence_allocate_ind#(adr0, istore0, ginval, gstore, gstore0, log1, m, ns0, true; istore, pstate; err1)⟩ ( abs-istore(avol0[n0, mapped(mkbuf(0))], lpt1, istore) ∧ abs-gstore(avol0[n0, mapped(mkbuf(0))], lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate = readonly ↔ pstate0 = readonly) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ err0 = err1), pstate = readonly, dups(log1)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt2[n0], m4, m5, lpf, m6]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt2[n0], m4, m5, lpf, m6