Nuprl Lemma : ctt-meaning-type_wf
∀[X:⊢''']. ∀[t:CttTerm]. (ctt-meaning-type{i:l}(X;t) ∈ 𝕌{i'''''})
Proof
Definitions occuring in Statement :
ctt-meaning-type: ctt-meaning-type{i:l}(X;t),
ctt-term: CttTerm,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ctt-meaning-type: ctt-meaning-type{i:l}(X;t),
ctt-term: CttTerm,
wfterm: wfterm(opr;sort;arity),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
isvarterm_wf,
ctt-op_wf,
ctt-term_wf,
cubical_set_wf,
cubical-type_wf,
cubical-term-eqcd,
equal-wf-T-base,
bool_wf,
assert_wf,
bnot_wf,
not_wf,
term-opr_wf,
eq_atom_wf,
ctt-op-sort_wf,
equal-wf-base,
set_subtype_base,
l_member_wf,
cons_wf,
nil_wf,
istype-atom,
atom_subtype_base,
composition-structure_wf,
istype-assert,
istype-void,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
assert_of_eq_atom,
iff_transitivity,
iff_weakening_uiff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
setElimination,
rename,
hypothesisEquality,
universeIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
cumulativity,
productEquality,
independent_isectElimination,
baseClosed,
applyEquality,
lambdaEquality_alt,
inhabitedIsType,
sqequalRule,
tokenEquality,
atomEquality,
equalityIstype,
sqequalBase,
functionIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
independent_pairFormation,
voidElimination
Latex:
\mforall{}[X:\mvdash{}''']. \mforall{}[t:CttTerm]. (ctt-meaning-type\{i:l\}(X;t) \mmember{} \mBbbU{}\{i'''''\})
Date html generated:
2020_05_21-AM-10_32_54
Last ObjectModification:
2020_05_02-PM-10_36_37
Theory : cubical!type!theory
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