Nuprl Lemma : id_perm_wf
∀T:Type. (id_perm() ∈ Perm(T))
Proof
Definitions occuring in Statement :
id_perm: id_perm(),
perm: Perm(T),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
id_perm: id_perm(),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
compose: f o g,
identity: Id,
tidentity: Id{T},
inv_funs: InvFuns(A;B;f;g),
and: P ∧ Q
Lemmas referenced :
mk_perm_wf_a,
identity_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
because_Cache,
hypothesis,
independent_functionElimination,
universeIsType,
universeEquality,
functionExtensionality_alt,
independent_pairFormation
Latex:
\mforall{}T:Type. (id\_perm() \mmember{} Perm(T))
Date html generated:
2019_10_16-PM-00_58_47
Last ObjectModification:
2018_10_08-AM-09_46_33
Theory : perms_1
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