Make the README correspond to the updated paper.

README.md

 # Iron: Managing Obligations in Higher-Order Concurrent Separation Logic
 
 This repository contains the Iron logic, as described in the POPL'19 paper
-"Iron: Managing Obligations in Higher-Order Concurrent Separation Logic" by
+"[Iron: Managing Obligations in Higher-Order Concurrent Separation Logic](https://iris-project.org/pdfs/2018-iron.pdf)" by
 Aleš Bizjak, Daniel Gratzer, Robbert Krebbers, and Lars Birkedal.
 
 ## Building Iron
@@ -163,71 +163,71 @@ are also defined using the fancy update modality. They may be found in
 
 ## A Correspondence of Theorems, Definitions, and Examples in the Paper to the Formalization
 
-While the correspondence between the contents of the paper and the
-formalization is discussed above, we have provided an explicit table
-for convenience.
-
-The format of the table is as follows: Name of
-Theorem/Rule/Definition/Proposition, the name in the formalization,
-and the file in the formalization.
-
-- The language definition in Section 2, `expr`, `theories/heap_lang/lang.v`
-- `e` and `↦`, `perm` and `↦`, `theories/heap_lang/heap.v`
-- Trackable invariants, `fcinv`, `theories/iron_logic/fcinv.v`
-- `OPerm(-, -)`, `fcinv_own`, `theories/iron_logic/fcinv.v`
-- `DPerm(-, -)`, `fcinv_cancel_own`, `theories/iron_logic/fcinv.v`
-- `HOARE-FRAME`, `hoare_frame_r`, `iris-coq/theories/program_logic/hoare.v`
-- `HOARE-VAL`, `ht_val`, `iris-coq/theories/program_logic/hoare.v`
-- `HOARE-λ`, `pure_rec`, `theories/heap_lang/lifting.v`
-- `HOARE-BIND`, `ht_bind`, `iris-coq/theories/program_logic/hoare.v`
-- `EMP-SPLIT`, `perm_split`, `theories/heap_lang/heap.v`
-- `PT-SPLIT`, `mapsto_uniform`, `theories/heap_lang/heap.v`
-- `PT-DISJ`, `mapsto_valid_2`, `theories/heap_lang/heap.v`
-- `HOARE-ALLOC`, `wp_alloc`, `theories/heap_lang/lifting.v`
-- `HOARE-FREE`, `wp_free`, `theories/heap_lang/lifting.v`
-- `HOARE-LOAD`, `wp_load`, `theories/heap_lang/lifting.v`
-- `HOARE-STORE`, `wp_store`, `theories/heap_lang/lifting.v`
-- `HOARE-FORK-EMP`/`HOARE-FORK-TRUE`, `wp_fork`, `theories/heap_lang/lifting.v`
-- `INV-DUP`, `inv_persistent`, `theories/heap_lang/lifting.v`
-- `INV-ALLOC`, `inv_alloc`, `iris-coq/theories/base_logic/lib/invariants.v`
-- `INV-OPEN`, `inv_open`, `iris-coq/theories/base_logic/lib/invariants.v`
-- `TINV-SPLIT`, `fcinv_own_fractional`, `theories/iron_logic/fcinv.v`
-- `TINV-DUP`, `fcinv_persistent`, `theories/iron_logic/fcinv.v`
-- `TINV-ALLOC`, `fcinv_alloc_named`, `theories/iron_logic/fcinv.v`
-- `TINV-OPEN`, `fcinv_open`, `theories/iron_logic/fcinv.v`
-- `TINV-DEALLOC`, `fcinv_cancel`, `theories/iron_logic/fcinv.v`
-- Uniform with respect to fractions, `Uniform`, `theories/iron_logic/iron.v`
-- `HOARE-CONS`, `ht_vs`, `iris-coq/theories/program_logic/hoare.v`
-- The rules from Figure 4, `head_step`, `theories/heap_lang/lang.v`
-- Theorem 2.1, `heap_adequacy`, `theories/heap_lang/adequacy.v`
-- Theorem 2.2, `heap_strong_adequacy`, `theories/heap_lang/adequacy.v`
-- `HOARE-PAR`, `par_spec`, `theories/heap_lang/lib/par.v`
-- The example from 3.1, `transfer_works1`, `theories/heap_lang/lib/resource_tranfer_par.v`
-- The example from 3.2, `transfer_works1`, `theories/heap_lang/lib/resource_tranfer_fork.v`
-- The example from 3.3, Several theorems, `theories/heap_lang/lib/message_passing.v`
-- The example from 3.4, `program_spec`, `theories/heap_lang/lib/message_passing_example.v`
-- The example from 3.5, Several theorems, `theories/heap_lang/lib/{spawn, par}.v`
-- Definitions of lifted connectives, Several definitions, `theories/bi/fracpred.v`
-- Definition of lifted `↦`, `↦`, `theories/heap_lang/heap.v`
-- `LHOARE-FRAME`, `iron_wp_frame_r`, `iris-coq/theories/program_logic/hoare.v`
-- `LHOARE-VAL`, `iron_wp_val`, `iris-coq/theories/program_logic/hoare.v`
-- `LHOARE-λ`, `pure_rec`, `theories/heap_lang/lifting.v`
-- `LHOARE-BIND`, `iron_wp_bind`, `iris-coq/theories/program_logic/hoare.v`
-- `LPT-DISJ`, `mapsto_valid_2`, `theories/heap_lang/heap.v`
-- `LHOARE-ALLOC`, `iron_wp_alloc`, `theories/heap_lang/lifting.v`
-- `LHOARE-FREE`, `iron_wp_free`, `theories/heap_lang/lifting.v`
-- `LHOARE-LOAD`, `iron_wp_load`, `theories/heap_lang/lifting.v`
-- `LHOARE-STORE`, `iron_wp_store`, `theories/heap_lang/lifting.v`
-- `LHOARE-FORK`, `iron_wp_fork`, `theories/heap_lang/lifting.v`
-- `LTINV-SPLIT`, `fcinv_own_fractional`, `theories/iron_logic/fcinv.v`
-- `LTINV-DUP`, `fcinv_persistent`, `theories/iron_logic/fcinv.v`
-- `LTINV-ALLOC`, `fcinv_alloc_named`, `theories/iron_logic/fcinv.v`
-- `LTINV-OPEN`, `fcinv_open`, `theories/iron_logic/fcinv.v`
-- `LTINV-DEALLOC`, `fcinv_cancel`, `theories/iron_logic/fcinv.v`
-- Definition of Hoare triples, `iron_wp`, `theories/iron_logic/weakestpre.v`
-- Theorem 4.1, `heap_adequacy`, `theories/heap_lang/adequacy.v`
-- Theorem 4.2, `heap_strong_adequacy`, `theories/heap_lang/adequacy.v`
-- Definition of WP in Section 5, `wp_def`, `iris-coq/theories/program_logic/weakestpre.v`
-- Definition of state interp from Section 5, `heap_ctx`, `theories/heap_lang/heap.v`
-- Theorem 5.1, `wp_strong_all_adequacy`, `iris-coq/theories/program_logic/adequacy.v`
-
+While the correspondence between the contents of the paper and the formalization
+is discussed above, we also provide an explicit table for convenience.
+
+| Paper definition or theorem |  Coq definition or theorem | File | 
+|-------|--------|---------|
+| The language definition in Sec. 3 | `expr` | `iron/theories/heap_lang/lang.v` |
+| `𝖊` and `↪` | `perm` and `↦` | `iron/theories/heap_lang/heap.v` |
+| Trackable invariants | `fcinv` | `iron/theories/iron_logic/fcinv.v` |
+| `OPerm(-, -)` | `fcinv_own` | `iron/theories/iron_logic/fcinv.v` |
+| `DPerm(-, -)` | `fcinv_cancel_own` | `iron/theories/iron_logic/fcinv.v` |
+| `HOARE-FRAME` | `hoare_frame_r` | `iris-coq/theories/program_logic/hoare.v` |
+| `HOARE-VAL` | `ht_val` | `iris-coq/theories/program_logic/hoare.v` |
+| `HOARE-λ` | `pure_rec` | `iron/theories/heap_lang/lifting.v` |
+| `HOARE-BIND` | `ht_bind` | `iris-coq/theories/program_logic/hoare.v` |
+| `EMP-SPLIT` | `perm_split` | `iron/theories/heap_lang/heap.v` |
+| `PT-SPLIT` | `mapsto_uniform` | `iron/theories/heap_lang/heap.v` |
+| `PT-DISJ` | `mapsto_valid_2` | `iron/theories/heap_lang/heap.v` |
+| `HOARE-ALLOC` | `wp_alloc` | `iron/theories/heap_lang/lifting.v` |
+| `HOARE-FREE` | `wp_free` | `iron/theories/heap_lang/lifting.v` |
+| `HOARE-LOAD` | `wp_load` | `iron/theories/heap_lang/lifting.v` |
+| `HOARE-STORE` | `wp_store` | `iron/theories/heap_lang/lifting.v` |
+| `HOARE-FORK-EMP`/`HOARE-FORK-TRUE` | `wp_fork` | `iron/theories/heap_lang/lifting.v` |
+| `INV-DUP` | `inv_persistent` | `iron/theories/heap_lang/lifting.v` |
+| `INV-ALLOC` | `inv_alloc` | `iris-coq/theories/base_logic/lib/invariants.v` |
+| `INV-OPEN` | `inv_open` | `iris-coq/theories/base_logic/lib/invariants.v` |
+| `TINV-SPLIT` | `fcinv_own_fractional` | `iron/theories/iron_logic/fcinv.v` |
+| `TINV-DUP` | `fcinv_persistent` | `iron/theories/iron_logic/fcinv.v` |
+| `TINV-ALLOC` | `fcinv_alloc_named` | `iron/theories/iron_logic/fcinv.v` |
+| `TINV-OPEN` | `fcinv_open` | `iron/theories/iron_logic/fcinv.v` |
+| `TINV-DEALLOC` | `fcinv_cancel` | `iron/theories/iron_logic/fcinv.v` |
+| Uniform with respect to fractions | `Uniform` | `iron/theories/iron_logic/iron.v` |
+| `HOARE-CONS` | `ht_vs` | `iris-coq/theories/program_logic/hoare.v` |
+| The rules from Figure 5 | `head_step` | `iron/theories/heap_lang/lang.v` |
+| Theorem 3.1 | `heap_basic_adequacy` | `iron/theories/heap_lang/adequacy.v` |
+| Theorem 3.2 | `heap_all_adequacy` | `iron/theories/heap_lang/adequacy.v` |
+| `HOARE-PAR` | `par_spec` | `iron/theories/heap_lang/lib/par.v` |
+| The example from 4.1 | `transfer_works1` | `iron/theories/heap_lang/lib/resource_transfer_par.v` |
+| The rules from Figure 6 | Several theorems | `iron/theories/heap_lang/lib/resource_transfer_sts.v` |
+| The example from 4.2 | `transfer_works1` | `iron/theories/heap_lang/lib/resource_transfer_fork.v` |
+| The example from 4.3 | Several theorems | `iron/theories/heap_lang/lib/message_passing.v` |
+| The queue specifications from 4.3 | Several theorems in Section `queue_bag_spec` | `iron/theories/heap_lang/lib/queue.v` |
+| The example from 4.4 | `program_spec` | `iron/theories/heap_lang/lib/message_passing_example.v` |
+| The example from 4.5 | Several theorems | `iron/theories/heap_lang/lib/{spawn,par}.v` |
+| Definitions of lifted connectives | Several definitions | `iron/theories/bi/fracpred.v` |
+| Definition of lifted `↦` | `↦` | `iron/theories/heap_lang/heap.v` |
+| `LHOARE-FRAME` | `iron_wp_frame_r` | `iris-coq/theories/program_logic/hoare.v` |
+| `LHOARE-VAL` | `iron_wp_val` | `iris-coq/theories/program_logic/hoare.v` |
+| `LHOARE-λ` | `pure_rec` | `iron/theories/heap_lang/lifting.v` |
+| `LHOARE-BIND` | `iron_wp_bind` | `iris-coq/theories/program_logic/hoare.v` |
+| `LPT-DISJ` | `mapsto_valid_2` | `iron/theories/heap_lang/heap.v` |
+| `LHOARE-ALLOC` | `iron_wp_alloc` | `iron/theories/heap_lang/lifting.v` |
+| `LHOARE-FREE` | `iron_wp_free` | `iron/theories/heap_lang/lifting.v` |
+| `LHOARE-LOAD` | `iron_wp_load` | `iron/theories/heap_lang/lifting.v` |
+| `LHOARE-STORE` | `iron_wp_store` | `iron/theories/heap_lang/lifting.v` |
+| `LHOARE-FORK` | `iron_wp_fork` | `iron/theories/heap_lang/lifting.v` |
+| `LTINV-SPLIT` | `fcinv_own_fractional` | `iron/theories/iron_logic/fcinv.v` |
+| `LTINV-DUP` | `fcinv_persistent` | `iron/theories/iron_logic/fcinv.v` |
+| `LTINV-ALLOC` | `fcinv_alloc_named` | `iron/theories/iron_logic/fcinv.v` |
+| `LTINV-OPEN` | `fcinv_open` | `iron/theories/iron_logic/fcinv.v` |
+| `LTINV-DEALLOC` | `fcinv_cancel` | `iron/theories/iron_logic/fcinv.v` | 
+| Definition of Hoare triples | `iron_wp` | `iron/theories/iron_logic/weakestpre.v` |
+| Theorem 5.1 | `heap_basic_adequacy` | `iron/theories/heap_lang/adequacy.v` |
+| Theorem 5.2 | `heap_all_adequacy` | `iron/theories/heap_lang/adequacy.v` |
+| Definition of WP in Section 6 | `wp_def` | `iris-coq/theories/program_logic/weakestpre.v` |
+| Definition of state interpretation from Section 6 | `heap_ctx` | `iron/theories/heap_lang/heap.v` |
+| Theorem 6.1 | `wp_strong_all_adequacy` | `iris-coq/theories/program_logic/adequacy.v` |
+| The lock specifications | Several theorems | `iron/theories/heap_lang/lib/spin_lock_track.v` |
+| Adequacy for the lock | `lock_always_freed` | `iron/theories/heap_lang/lib/spin_lock_track.v` |