Nuprl Lemma : update-context4_wf
∀[X:?CubicalContext]
∀[phi:Provisional''''(cttTerm(context-set(X)))]. (update-context4{i:l}(X;phi) ∈ ?CubicalContext)
supposing context-ok(X)
Proof
Definitions occuring in Statement :
update-context4: update-context4{i:l}(X;phi),
context-set: context-set(ctxt),
context-ok: context-ok(ctxt),
cubical-context: ?CubicalContext,
ctt-term-meaning: cttTerm(X),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
provisional-type: Provisional(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
update-context4: update-context4{i:l}(X;phi),
cubical-context: ?CubicalContext,
context-ok: context-ok(ctxt),
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
istype: istype(T),
cubical_context: CubicalContext,
squash: ↓T,
context-set: context-set(ctxt),
all: ∀x:A. B[x],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cubical_context_wf,
allow_wf,
provisional-type_wf,
ctt-term-meaning_wf,
context-set_wf,
context-ok_wf,
cubical-context_wf,
bind-provision_wf,
restrict-cubical-context_wf,
provisional-subtype,
pi1_wf_top,
cubical_set_wf,
subtype_rel-equal,
equal_wf,
squash_wf,
true_wf,
istype-universe,
istype-top,
subtype_rel_product,
list_wf,
varname_wf,
l_member_wf,
top_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
setIsType,
universeIsType,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
productIsType,
because_Cache,
equalityIstype,
hypothesisEquality,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
independent_isectElimination,
cumulativity,
lambdaEquality_alt,
setElimination,
rename,
productElimination,
applyEquality,
independent_pairEquality,
Error :memTop,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productEquality,
functionEquality,
setEquality,
lambdaFormation_alt,
functionIsType,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[X:?CubicalContext]
\mforall{}[phi:Provisional''''(cttTerm(context-set(X)))]. (update-context4\{i:l\}(X;phi) \mmember{} ?CubicalContext)
supposing context-ok(X)
Date html generated:
2020_05_20-PM-08_15_02
Last ObjectModification:
2020_05_19-AM-01_22_25
Theory : cubical!type!theory
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