}
]
class "grass"
- [ { "natural numbers with infinity" * } {
- [ { "" * } {
- [ "ynat ( ∞ )" "ynat_pred ( ↓? )" "ynat_succ ( ↑? )"
- "ynat_le ( ? ≤ ? )" "ynat_lt ( ? < ? )"
- "ynat_plus ( ? + ? )" "ynat_minus_sn ( ? - ? )" *
- ]
+ [ { "arithmetics" * } {
+ [ { "extensions" * } {
+ [ "arith_2a ( 𝟐 )" "arith_2b" * ]
+ }
+ ]
+ [ { "well-founded induction" * } {
+ [ "wf1_ind_ylt" * ]
+ [ "wf1_ind_nlt" "wf2_ind_nlt" "wf3_ind_nlt.ma" * ]
+ }
+ ]
+ [ { "non-negative integers with infinity" * } {
+ [ "ynat_lt ( ?<? )" "ynat_lt_succ" "ynat_lt_pred" "ynat_lt_pred_succ" "ynat_lt_plus" "ynat_lt_plus_pred" "ynat_lt_minus1" "ynat_lt_minus1_plus" "ynat_lt_le" "ynat_lt_le_succ" "ynat_lt_le_pred" "ynat_lt_le_pred_succ" "ynat_lt_le_plus" "ynat_lt_le_minus1" "ynat_lt_le_minus1_plus" * ]
+ [ "ynat_le ( ?≤? )" "ynat_le_succ" "ynat_le_pred" "ynat_le_pred_succ" "ynat_le_plus" "ynat_le_minus1" "ynat_le_minus1_succ" "ynat_le_minus1_plus" * ]
+ [ "ynat_minus1 ( ?-? )" "ynat_minus1_succ" "ynat_minus1_plus" * ]
+ [ "ynat_plus ( ?+? )" * ]
+ [ "ynat_pred ( ↓? )" "ynat_pred_succ" * ]
+ [ "ynat_succ ( ↑? )" * ]
+ [ "ynat ( 𝟎 ) ( ∞ )" "ynat_nat" * ]
}
]
- }
- ]
- class "grass"
- [ { "arithmetics" * } {
[ { "non-negative integers" * } {
[ "nat_lt ( ?<? )" "nat_lt_tri" "nat_lt_pred" "nat_lt_plus" "nat_lt_minus" "nat_lt_minus_plus" * ]
[ "nat_le ( ?≤? )" "nat_le_pred" "nat_le_plus" "nat_le_minus" "nat_le_minus_plus" "nat_le_max" * ]
]
[ { "positive integers" * } {
[ "pnat_plus ( ?+? )" * ]
- [ "pnat ( 𝟏 ) ( ↑? )" "pnat_dis" "pnat_iter ( ?^{?}? )" *"pnat_tri" ]
+ [ "pnat ( 𝟏 ) ( ↑? )" "pnat_dis" "pnat_iter ( ?^{?}? )" "pnat_tri" * ]
}
]
}
[ { "" * } {
[ "stream ( ? ⨮{?} ? )" "stream_eq ( ? ≗{?} ? )" "stream_hdtl ( ⫰{?}? )" "stream_tls ( ⫰*{?}[?]? )" * ]
[ "list ( Ⓔ{?} ) ( ? ⨮{?} ? )" "list_length ( |?| )" * ]
- [ "bool ( Ⓕ ) ( Ⓣ )" "arith ( ?^? ) ( ↑? ) ( ↓? ) ( ? ∨ ? ) ( ? ∧ ? )" "arith_2a" "arith_2b" * ]
+ [ "bool ( Ⓕ ) ( Ⓣ )" * ]
[ "ltc" "ltc_ctc" * ]
[ "logic ( ⊥ ) ( ⊤ )" "relations ( ? ⊆ ? )" "functions" "exteq ( ? ≐{?,?} ? )" "star" "lstar_2a" * ]
}
]
class "orange"
[ { "generated library" * } {
- [ { "well-founded induction" * } {
- [ "wf1_ind_nlt" "wf2_ind_nlt" "wf3_ind_nlt.ma" * ]
- }
- ]
[ { "generalization with equality" * } {
[ "insert_eq" * ]
}