diff options
| author | Tanaka Akira | 2019-02-19 11:29:16 +0900 |
|---|---|---|
| committer | Tanaka Akira | 2019-02-19 11:29:16 +0900 |
| commit | 6031ab6f20bc2fb160ce5a47ab34f34c6cd25e5e (patch) | |
| tree | a5c4bf710cd379613c2cfd17ffcf0c3ca2e6acb1 | |
| parent | 65ac4f973d59b083db965ea393ead27c9b1e5a5e (diff) | |
Make the conclusion of local contexts W-Ind empty.
The conclusion of W-Ind,
"\WF{E;~\ind{p}{Γ_I}{Γ_C}}{Γ}", is changed to
"\WF{E;~\ind{p}{Γ_I}{Γ_C}}{}" because
local contexts should be empty when
inductive definition is defined globally.
This is consistent with W-Global-Assum and W-Global-Def.
The side condition "c_i ∉ Γ ∪ E" which I changed previous commit is
changed again to "c_i ∉ E" because I guess that it tries to
avoid name conflicts to the local contexts in the conclusion.
However, the condition is useless after the local contexts is empty.
| -rw-r--r-- | doc/sphinx/language/cic.rst | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index ae6ca18f92..775fc76cfe 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -965,7 +965,7 @@ such that :math:`Γ_I` is :math:`[I_1 :∀ Γ_P ,A_1 ;~…;~I_k :∀ Γ_P ,A_k]` \WFE{Γ_P} (E[Γ_I ;Γ_P ] ⊢ C_i : s_{q_i} )_{i=1… n} ------------------------------------------ - \WF{E;~\ind{p}{Γ_I}{Γ_C}}{Γ} + \WF{E;~\ind{p}{Γ_I}{Γ_C}}{} provided that the following side conditions hold: @@ -975,7 +975,7 @@ provided that the following side conditions hold: context of parameters, + for :math:`j=1… k` we have that :math:`A_j` is an arity of sort :math:`s_j` and :math:`I_j ∉ E`, + for :math:`i=1… n` we have that :math:`C_i` is a type of constructor of :math:`I_{q_i}` which - satisfies the positivity condition for :math:`I_1 … I_k` and :math:`c_i ∉ Γ_I ∪ E`. + satisfies the positivity condition for :math:`I_1 … I_k` and :math:`c_i ∉ E`. One can remark that there is a constraint between the sort of the arity of the inductive type and the sort of the type of its |